Simplify 8C5
A 6,720
B 336
C 56
D 10
pls helpp
2 answers
8! / [(8 - 5)! * 5!]
The factorial definition is great, but I have often found it convenient that to find nCr, note two things.
(1) if r > n/2, then ncR = nC(n-r)
For example, 20C17 = 20C3
This makes it easier to evaluate
(2) write the fraction by counting down from n in the numerator, and counting up from 1 in the denominator. Count for r factors.
20C3 = 20*19*18 / 1*2*3 = 20*19*6*3 / 1*2*3 = 20*19*3
It is easy to split out factors that cancel out in the denominator
Note that 20C17 = 20*19*18*17*16*...*4 / 1*2*3*4*...*17
Note that the last 14 factors cancel directly, showing that 20C17 = 20C3
(1) if r > n/2, then ncR = nC(n-r)
For example, 20C17 = 20C3
This makes it easier to evaluate
(2) write the fraction by counting down from n in the numerator, and counting up from 1 in the denominator. Count for r factors.
20C3 = 20*19*18 / 1*2*3 = 20*19*6*3 / 1*2*3 = 20*19*3
It is easy to split out factors that cancel out in the denominator
Note that 20C17 = 20*19*18*17*16*...*4 / 1*2*3*4*...*17
Note that the last 14 factors cancel directly, showing that 20C17 = 20C3