Help If you are good at Algebra?

Question

What is the number of distinct 4-person committees that can be chosen from a group of 6 people?

Answer 1

out of 6 choose 4 then use:
₆C₄
if you don't have such a button on your calculator then:

₆C₄ = 6! / ((6-4)!*4!) = 15

for a better understanding try this:
you have persons A,B,C,D,E,F (six people) and you pick 4, your distinct choices are:

ABCD, ABCE, ABCF, ABDE, ABDF, ABEF, ACDE, ACDF, ACEF, ADEF, BCDE, BCDF, BCEF, BDEF, CDEF

out of 720 possibilities, many of them duplicates of each other in different order like:

ABCF, CBAF, FACB,FCAB, ACFB, AFBC, AFCB etc...

these are all the same panel, they were just picked in a different order, so they have to be eliminated. to do this we divide by, (6-4)!*4!, leaving us with only the distict choices.

if the question had stated the order of picking mattered then 720 or 6! would have been your answer.

To have a little more fun with this and get the concept and use an online calculator for your question, check the site below:

Answer 2

I guess its 6C4 which is equal to 15

Answer 3

there were about 60 I could come up with, but I'm not sure about my formula for this..