https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:permutations-and-combinations-ncert-new/x0419e5b3b578592a:untitled-896/v/fundamental-principle-of-counting 2025-03-01T15:52:37.13987578Z Fundamental principle of counting In this video, we cover the fundamental principles of counting. We realise through the examples discussed in this video that the principle is all about AND and OR. We learn through non-math examples, how we can slow down our thinking process and break individual steps apart. As we move along the examples shown in the video, we get familiar with the vocabulary of AND (multiplication) and OR (addition) which we'll use throughout this chapter. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Fundamental principle of counting In this video, we cover the fundamental principles of counting. We realise through the examples discussed in this video that the principle is all about AND and OR. We learn through non-math examples, how we can slow down our thinking process and break individual steps apart. As we move along the examples shown in the video, we get familiar with the vocabulary of AND (multiplication) and OR (addition) which we'll use throughout this chapter. https://cdn.kastatic.org/ka-youtube-converted/HDLBCv4yyIs.mp4/HDLBCv4yyIs.mp4 560 Counting elements of a set https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:permutations-and-combinations-ncert-new/x0419e5b3b578592a:untitled-896/v/using-and-and-or 2025-03-01T15:52:37.13987578Z Using AND and OR In this video, we use the concept of AND and OR to solve problems involving rearrangement of digits. We discuss both scenarios: repetition allowed and not allowed. For the first scenario, we take 5 digits and try to create as many 3 digit numbers as possible using these digits. Since the repetition is not allowed, we realise that we get different number of ways to perform individual tasks. This is not the case for the second problem discussed where the repetition is allowed. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Using AND and OR In this video, we use the concept of AND and OR to solve problems involving rearrangement of digits. We discuss both scenarios: repetition allowed and not allowed. For the first scenario, we take 5 digits and try to create as many 3 digit numbers as possible using these digits. Since the repetition is not allowed, we realise that we get different number of ways to perform individual tasks. This is not the case for the second problem discussed where the repetition is allowed. https://cdn.kastatic.org/ka-youtube-converted/EswVjS-KwLQ.mp4/EswVjS-KwLQ.mp4 401 Counting elements of a set https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:permutations-and-combinations-ncert-new/x0419e5b3b578592a:untitled-896/v/using-and-and-or-with-constraints-permutations-and-combinations 2025-05-31T02:32:31.283700489Z Using AND and OR (with constraints) This video tackles problems involving arrangements of digits where we have to take care of constraints. Problems involving even and odd numbers are picked as examples. We first solve for the scenario where repetition is allowed before moving to the scenario where repetition is not allowed. This is where we keep getting stuck until we realise the issue of constraints and the importance of prioritisation. Finally, we figure out the correct approach to solve such problems! Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Using AND and OR (with constraints) This video tackles problems involving arrangements of digits where we have to take care of constraints. Problems involving even and odd numbers are picked as examples. We first solve for the scenario where repetition is allowed before moving to the scenario where repetition is not allowed. This is where we keep getting stuck until we realise the issue of constraints and the importance of prioritisation. Finally, we figure out the correct approach to solve such problems! https://cdn.kastatic.org/ka-youtube-converted/kjaba1lWikM.mp4/kjaba1lWikM.mp4 522 Counting elements of a set https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:permutations-and-combinations-ncert-new/x0419e5b3b578592a:untitled-896/v/we-using-and-and-or-constraints 2025-03-01T15:52:37.13987578Z WE - Using AND and OR (constraints) In this video, we solve some worked examples involving problems related to rearrangement of digits with constraints. We first find even numbers for both scenarios - repetition allowed and repetition not allowed. We then solve a similar problem where we need to find the total number of odd numbers. We then solve a problem where we need to find the total number of telephone numbers. Important thing to note is that telephone numbers have no problem starting with zero. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw WE - Using AND and OR (constraints) In this video, we solve some worked examples involving problems related to rearrangement of digits with constraints. We first find even numbers for both scenarios - repetition allowed and repetition not allowed. We then solve a similar problem where we need to find the total number of odd numbers. We then solve a problem where we need to find the total number of telephone numbers. Important thing to note is that telephone numbers have no problem starting with zero. https://cdn.kastatic.org/ka-youtube-converted/WRTWrIEkfCw.mp4/WRTWrIEkfCw.mp4 450 Counting elements of a set https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:permutations-and-combinations-ncert-new/x0419e5b3b578592a:untitled-896/v/curious-case-of-0 2025-03-01T15:52:37.13987578Z Curious case of 0 This video tackles the case where a digit is torn between two conflicting constraints. We try to make two digit numbers using a set of digits that include 0. We first solve for a case where repetition is allowed. We run into problems where repetition is not allowed - even though we are dealing with the last digit constraint. We quickly realise that the issue is not with the boxes but with the digit zero. We arrive at a neat solution involving cases and use it to solve another similar practice problem. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Curious case of 0 This video tackles the case where a digit is torn between two conflicting constraints. We try to make two digit numbers using a set of digits that include 0. We first solve for a case where repetition is allowed. We run into problems where repetition is not allowed - even though we are dealing with the last digit constraint. We quickly realise that the issue is not with the boxes but with the digit zero. We arrive at a neat solution involving cases and use it to solve another similar practice problem. https://cdn.kastatic.org/ka-youtube-converted/mBr3c54Vhgk.mp4/mBr3c54Vhgk.mp4 533 Counting elements of a set https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-probability-statistics/cc-7th-compound-events/e/fundamental-counting-principle 2026-03-26T05:20:35.16058035Z The counting principle Practice counting possible outcomes in a variety of situations. These problems cover everything from counting the number of ways to get dressed in the morning to counting the number of ways to build a custom pizza. Ben S exercise https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:permutations-and-combinations-ncert-new/x0419e5b3b578592a:untitled-896/e/and-or-fundamental-principle-of-counting 2025-06-08T10:10:13.650905119Z AND/OR: Fundamental principle of counting AND/OR: Fundamental principle of counting Ashish Gupta exercise https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:permutations-and-combinations-ncert-new/x0419e5b3b578592a:untitled-896/e/using-and-or-digits-with-constraints 2025-06-08T10:10:13.650905119Z Using AND/OR (digits with constraints) Using AND/OR (digits with constraints) Ashish Gupta exercise https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:permutations-and-combinations-ncert-new/x0419e5b3b578592a:untitled-896/e/and-or-dealing-with-the-digit-zero 2025-05-31T02:32:31.283700489Z AND/OR: dealing with the digit zero AND/OR: dealing with the digit zero Ashish Gupta exercise