(A) How many ways can a 2-person subcommittee be selected from a committee of 8 people? (B) How many ways can a president and vice-president be chosen from a committee of 8 people?

28, 56

56

Step-by-step explanation:

a

To solve this, we use the combination rule.

nCk = n!/k!(n-k)! where

n is the number of options (8) k is the number of slots (2).

Assuming the order doesn't matter, then

8C2 = 8! / 2!(8-2)!

8C2 = 8! / 2! 6!

8C2 = 40320 / 2 * 720

8C2 = 40320 / 1440

8C2 = 28

If the order does matter, then we use permutation instead.

nPk = n!/(n-k!) where n = 8 and k =2 8P2 = 8! / 6!

8P2 = 40320 / 720

8P2 = 56

b

We are told that there exist 8 ways to choose a president and a vice president. This means that, after choosing a president from 8 people, there remains 7 people to choose his vice from. Thus, the number of ways to choose a president and his vice are 8 * 7 = 56

one of each metals

step-by-step explanation:

x=17

step-by-step explanation:

solve 3x-24=x+10

then that makes it 2x=34 because you subtract an x from both sides to get rid of the one on the right, and then you add 24 to both sides to get rid of the 24 on the left

divide by both sides by 2 to get your answer so that you can get your answer