(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

a mantle plume is an upwelling of abnormally hot rock within the earth's mantle. as the heads of mantle plumes can partly melt when they reach shallow depths, they are thought to be the cause of volcanic centers known as hotspots and probably also to have caused flood basalts.

step-by-step explanation:

the answer to this in exact form is 4/35 but in decimal form its 0.1142857

hope this if needed hmu