Question

How many different committees of 4 people can be chosen from a group of 21?


143,640
5,985
1,9955

Answer 1

i believe you use combination
\[\LARGE \frac{n!}{r!(n-r)!}\]
therefore you have
\[\LARGE \frac{21!}{4!(21-4)!}\]

Answer 2

woud it be A then?

Answer 3

A is just \[21 \times 20 \times 19 \times 18\]
you have to divide htat by \[4 \times 3 \times 2\] to get the final answer

Answer 4

i still don't understand

Answer 5

there are only 4 spots. you have 21 choices for the first spot, then 20 for the second, 19 for the third and 18 for the fourth. you don't want any of the groups to repeat so dividing by 4! will divide out the repeater groups.

The multiplication of the numbers is the how many ways all together the group can be chosen.

Do a search for basic counting methods and combinatorics to further your knowledge on the subject. A knowing of factorials and how their applied is very necessary.