Question

​(A) How many ways can a 3​-person subcommittee be selected from a committee of 6 ​people? ​(B) How many ways can a president comma vice dash president comma and secretary be chosen from a committee of 6 ​people?

Answer 1

Answer:

A) N = 20 ways

a 3​-person subcommittee can be selected from a committee of 6 ​people in 20 ways.

B)N = 120 ways

The president, vice president and secretary can be chosen from a committee of 6 ​people in 120 ways.

Step-by-step explanation:

A) the number of ways a 3​-person subcommittee be selected from a committee of 6 ​people N;

Since there is no given order for the selection, this means that the order of selection is irrelevant. Therefore, this is a combination problem where order is not considered.

N = nCr

N = 6C3

N = 6!/3!(6-3)! = 6!/3!3!

N = 720/(6×6)

N = 20 ways

a 3​-person subcommittee can be selected from a committee of 6 ​people in 20 ways.

B) the number of ways a president, vice president and secretary can be chosen from a committee of 6 ​people N;

In this case, there is a given order of selection for the 3 posts. This is a permutation.

N = nPr

N = 6P3

N = 6!/(6-3)!

N = 6!/3!

N = 120 ways

The president, vice president and secretary can be chosen from a committee of 6 ​people in 120 ways.