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### Course: Pixar in a Box>Unit 13

Lesson 2: Counting crowds

# 6. Binomial coefficient

Get ready for a really powerful formula: the binomial coefficient! The binomial coefficient allows us to calculate the number of ways to select a small number of items from a larger group. The formula is represented as n choose k equals n! divided by k!(n-k)!. We can use it to solve problems like determining the number of possible casts from a group of actors.

## Want to join the conversation?

• I'm bad at math so i give up but i'm still trying so hard but i try a little but i can't
• on i dont get why our 6! / 3! became 6! / 3! * 3! ? where did the second 3! come from?
• That's because we need to divide by 3! to account for the 6 different permutations.

Remember it's: # combinations / # permutations.

# combinations = 6x5x4 = 6!/3!
# permutations = 3!

Let me know if you need more help
• It's so famous because its so complicated! How do permutations work again?
• how to do the choose on a calculator
• Hi guys! Is it true that if k=0, the binomial coefficient equals 1? If so, then why? Thnx
• At , if it's been a while since you took algebra, the reason n-(k-1) = n-k+1 is the distributive property. Not really a question, but it's something I had to look up and no one else asked it.
• would that mean 6! = 3!*3! ?
• No.
6!=6*5*4*3*2*1=720
3!=3*2*1=6
3!3!=3*2*1*3*2*1=36
(1 vote)
• I don't quite understand how this stuff works, any other videos i could watch first?
(i have seen allof the videos in this section)