https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:permutations-and-combinations-ncert-new/x0419e5b3b578592a:untitled-908/v/intro-to-combinations-1 2025-05-22T11:09:14.016569349Z Intro to Combinations In this video, we look at an interesting way to find the number of selections from a given set of distinct objects. We use the word NATURE as an example. We know how to find the ways to form a given lettered word. But we break this process down into its two parts - selecting and arranging. We divide the total number of words by the number of ways of arranging letters to get the number of ways of selecting. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Intro to Combinations In this video, we look at an interesting way to find the number of selections from a given set of distinct objects. We use the word NATURE as an example. We know how to find the ways to form a given lettered word. But we break this process down into its two parts - selecting and arranging. We divide the total number of words by the number of ways of arranging letters to get the number of ways of selecting. https://cdn.kastatic.org/ka-youtube-converted/Zryrco_IrsA.mp4/Zryrco_IrsA.mp4 418 Solving problems involving combinations of objects https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:permutations-and-combinations-ncert-new/x0419e5b3b578592a:untitled-908/v/formulae-for-permutation-combination 2025-05-22T11:09:14.016569349Z Formulae for Permutation & Combination In this video, we look at the formula for permutations and combinations of r distinct objects out of n distinct objects. We look at a convenient way to find number of combinations. We then practice using the formulae and observe a few key results. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Formulae for Permutation & Combination In this video, we look at the formula for permutations and combinations of r distinct objects out of n distinct objects. We look at a convenient way to find number of combinations. We then practice using the formulae and observe a few key results. https://cdn.kastatic.org/ka-youtube-converted/W7jYJTCjuko.mp4/W7jYJTCjuko.mp4 584 Solving problems involving combinations of objects https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:permutations-and-combinations-ncert-new/x0419e5b3b578592a:untitled-908/v/equations-involving-formulae-of-pnc 2025-05-22T11:09:14.016569349Z Equations involving formulae of PnC In this video, we solve four equations involving permutations and combinations. For the first one, we apply the result we observed in the previous video - combination of r objects is same as that of n-r objects. For the remaining three, we plug in the formulae for ncr and npr and solve for the missing variable. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Equations involving formulae of PnC In this video, we solve four equations involving permutations and combinations. For the first one, we apply the result we observed in the previous video - combination of r objects is same as that of n-r objects. For the remaining three, we plug in the formulae for ncr and npr and solve for the missing variable. https://cdn.kastatic.org/ka-youtube-converted/UrilH1jF_JU.mp4/UrilH1jF_JU.mp4 436 Solving problems involving combinations of objects https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:permutations-and-combinations-ncert-new/x0419e5b3b578592a:untitled-908/v/finding-number-of-combinations 2025-05-22T11:09:14.016569349Z Finding number of combinations In this video, we practice finding number of ways to select from a given set of distinct objects. We first select a team of some boys and girls. We then select balls of different colors from a given set. We then form a cricket team comprising of a given number of bowlers using a given set of players. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Finding number of combinations In this video, we practice finding number of ways to select from a given set of distinct objects. We first select a team of some boys and girls. We then select balls of different colors from a given set. We then form a cricket team comprising of a given number of bowlers using a given set of players. https://cdn.kastatic.org/ka-youtube-converted/vFp0BkWQUlY.mp4/vFp0BkWQUlY.mp4 469 Solving problems involving combinations of objects https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:permutations-and-combinations-ncert-new/x0419e5b3b578592a:untitled-908/v/number-of-ways-of-forming-groups 2025-05-22T11:09:14.016569349Z Number of ways of forming groups In this video, we solve two problems of forming groups with given constraints on selections. We realise that we need to consider all possible cases which are satisfied by the constraint and add the number of ways for each of them. For the first one, we form teams of boys and girls for three different scenarios - the team has no girls, has at least one boy and one girl, and has at least three girls. For the second one, the constraints are - exactly 3 girls, at least 3 girls, and at most 3 girls. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Number of ways of forming groups In this video, we solve two problems of forming groups with given constraints on selections. We realise that we need to consider all possible cases which are satisfied by the constraint and add the number of ways for each of them. For the first one, we form teams of boys and girls for three different scenarios - the team has no girls, has at least one boy and one girl, and has at least three girls. For the second one, the constraints are - exactly 3 girls, at least 3 girls, and at most 3 girls. https://cdn.kastatic.org/ka-youtube-converted/imxAo-yWwsE.mp4/imxAo-yWwsE.mp4 546 Solving problems involving combinations of objects https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:permutations-and-combinations-ncert-new/x0419e5b3b578592a:untitled-908/v/multiple-selections 2025-05-22T11:09:14.016569349Z Multiple selections In this video, we solve 3 problems of arranging distinct objects in a row given constraints on arrangements. We realise that it is better to split the tasks and tackle the ones that don't involve constraints first. We first solve for a scenario where boys and girls are seated in a row but no two boys sit together. In the second one, the girls are sitting in even places. For the last one, we arrange + and - signs such that no two - signs are together. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Multiple selections In this video, we solve 3 problems of arranging distinct objects in a row given constraints on arrangements. We realise that it is better to split the tasks and tackle the ones that don't involve constraints first. We first solve for a scenario where boys and girls are seated in a row but no two boys sit together. In the second one, the girls are sitting in even places. For the last one, we arrange + and - signs such that no two - signs are together. https://cdn.kastatic.org/ka-youtube-converted/jrvbAg5wlQY.mp4/jrvbAg5wlQY.mp4 367 Solving problems involving combinations of objects https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:permutations-and-combinations-ncert-new/x0419e5b3b578592a:untitled-908/v/applications-of-pnc-in-geometry 2025-05-22T11:09:14.016569349Z Applications of PnC in Geometry In this video, we apply the concepts of permutations and combination to the world of geometry. We find out how many lines pass through a given number of non-collinear points. We then figure out the number of diagonals using the number of sides of the polygon. We also figure out the number of triangles formed using a given number of non-collinear points. Finally, we tackle the case of collinearity. What happens if some points are collinear and rest are not? Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Applications of PnC in Geometry In this video, we apply the concepts of permutations and combination to the world of geometry. We find out how many lines pass through a given number of non-collinear points. We then figure out the number of diagonals using the number of sides of the polygon. We also figure out the number of triangles formed using a given number of non-collinear points. Finally, we tackle the case of collinearity. What happens if some points are collinear and rest are not? https://cdn.kastatic.org/ka-youtube-converted/MAkIfEevAEs.mp4/MAkIfEevAEs.mp4 401 Solving problems involving combinations of objects https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:permutations-and-combinations-ncert-new/x0419e5b3b578592a:untitled-908/e/intro-to-combinations 2025-05-31T02:32:31.283700489Z Intro to Combinations Intro to Combinations Ashish Gupta exercise https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:permutations-and-combinations-ncert-new/x0419e5b3b578592a:untitled-908/e/formulae-for-pnc 2025-05-31T02:32:31.283700489Z Formulae for PnC Formulae for PnC Ashish Gupta exercise https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:permutations-and-combinations-ncert-new/x0419e5b3b578592a:untitled-908/e/equations-involving-pnc 2025-05-31T02:32:31.283700489Z Equations involving PnC Equations involving PnC Ashish Gupta exercise https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:permutations-and-combinations-ncert-new/x0419e5b3b578592a:untitled-908/e/number-of-ways-of-forming-groups 2025-05-31T02:32:31.283700489Z Number of ways of forming groups Number of ways of forming groups Ashish Gupta exercise https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:permutations-and-combinations-ncert-new/x0419e5b3b578592a:untitled-908/e/multiple-selections 2025-05-31T02:32:31.283700489Z Multiple selections Multiple selections Ashish Gupta exercise https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:permutations-and-combinations-ncert-new/x0419e5b3b578592a:untitled-908/e/applications-of-pnc-in-geometry 2025-05-31T02:32:31.283700489Z Applications of PnC in Geometry Applications of PnC in Geometry Ashish Gupta exercise