Calculating Binomial Coefficients
What is nC1? (Give a formula in terms of n)
n
What is nC0 for any n?
1
On what row is the very top number of Pascal's Triangle in?
Row 0
What is 3!
6
What is 8C2?
28
What is nCn for any n?
1
How many numbers are in the nth row?
n+1
What is 5!
120
What is 10C3?
120
What is nCk equal to for any n,k? (Your answer should be in the form xCy for x,y in terms of n,k)
nC(n-k)
How many rows does Pascal's Triangle have?
Infinity
What is 7!
5040
What is 15C6?
5005
What is nC0 + nC1 + nC2 + nC3 + ... + nCn equal to? (Give a formula in terms of n)
2^n
Who invented Pascal's Triangle at least one thousand years before Pascal did?
The Chinese
What is 8!
40320
What is nC3? (Give a formula in terms of n)
n(n-1)(n-2)/6
What is nC0 + nC2 + nC4 + ... equal to? (Give a formula in terms of n. The choose function only adds the EVEN numbers)
2^(n-1)
What does nCk represent on Pascal's Triangle? (Specifically, what does it count?)
The number of paths from the top number to nCk
362880