Pascal's triangle/factorals question?

Question

Write a forumla for calculating:
( m
n )
using factorals and how it relates to row 5 in Pascal's triangle.



Is the formula:
m! / n! (m-n)!

And how does it relate?

Answer 1

Yes, it is, and the relation is that, if you number the elements in the triangle from 0, 5Cn is precisely the value of the nth element of the 5th row. i.e. 5C0=1, 5C1=5, 5C2=10, 5C3=10, 5C4=5, and 5C5 = 1.

Answer 2

Your formula is correct.

row 5 of Pascal's triangle is: C(5,0), C(5,1), C(5,2), C(5,3), C(5,4), C(5,5)

Where
C(m,n) =
(m
n)