bakfed wrote:
brinng back an old post.
I somehow can't get 20C5/20C4 to be 16/5; I keep on getting 8/5
Also, for this question, why can't we just do the following:
(20*19*18*17*16)/(20*19*18*17) = 16/1?
\(\frac{C^5_{20}}{C^4_{20}}=\frac{20!}{15!*5!}*\frac{16!*4!}{20!}=\frac{16}{5}\)
Second question:
20*19*18*17*16 does not give you # of 5 member committees out of 20. You need to divide this by 5! to get rid of the repetitions (factorial correction). The same for 20*19*18*17, you should divide this by 4!.
Take another example: how many committees of 2 can be formed out of A, B and C?
AB
AC
BC
Only 3, which is \(C^2_3=3\).
But the way you are doing you'd get 3*2=6. This number has repetitions so we should divide it by 2! --> 6/2!=3.
Hope it's clear.
hey I got the correct answer but was just wondering why the members have to be different, i.e. why we are using combinations ?
I hate long and complicated explanations!