(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

answer: the answer is one of

step-by-step explanation:   we are given to write a proper fraction where the whole is divided into an even number of equal parts less than ten, and an odd number of those parts exist.

an even number less than 10 may be one of 2, 4, 6 or 8. so, the whole may be one of these four evens.

now, an odd number of these parts must exist, so the numerator must be an odd number, one of 1, 3, 5 or 7. it cannot be 9 because then the fraction will become improper.

thus, our fraction may be one of the following