Question

determine if the situation involves a permutation or a combination and then find the answer
a.in how many ways can 12 members of a jury be selected from a jury pool of 150 ?
b.in how many ways can a foreman , assistant foreman and secretary be selected from a 12-member group ?

Answer 1

a)
In this case, it doesn't matter the order that the jury members are selected in... for example if Jon is picked first and Jake picked second, this is no different than Jake picked first and Jon picked second, because in the end Jon and Jake are in the jury.

Answer 2

When order doesn't matter, you want to use combinations.

Answer 3

So for a) we have \[
\binom{150}{12}
\]

Answer 4

b)
IN this case, order does matter. We think of it as choosing 3 members.. first is foreman, second is assistant foreman, third is secretary. If Jon is picked first, his is different than if Jon is picked second, because in one case John is a foreman and in the other case he is an assistant foreman... these are distinct outcomes.

Answer 5

So for B we have \[
P(12,3) = \frac{12!}{(12-3)!}
\]

Answer 6

For A we have \[
\binom{150}{12} = \frac{150!}{12!(150-12)!}
\]

Answer 7

ty :)