Question

How many ways can a 4​-person subcommittee be selected from a committee of 6 ​people? ​(B) How many ways can a president comma vice dash president comma secretary comma and treasurer be chosen from a committee of 6 ​people?

Answer 1

A) 360

B) 360

Explanation:

Part A)

Given that there are a total of 6 people and 4 person subcommittee is to be selected.

Number of ways to select 1st person = 6

Now, 1 person is selected, total persons left are 5

Number of ways to select 2nd person = 5

Now, 1 person is selected, total persons left are 4

Number of ways to select 3rd person = 4

Now, 1 person is selected, total persons left are 3

Number of ways to select 4th person = 3

So, total number of ways = 6
`*`5
`*`4
`*`3 = 360

Part B)

Given that there are a total of 6 people in the committee

Number of ways to select president = 6

Now, 1 person is selected, total persons left are 5

Number of ways to select vice president = 5

Now, 1 person is selected, total persons left are 4

Number of ways to select secretary = 4

Now, 1 person is selected, total persons left are 3

Number of ways to select treasurer = 3

So, total number of ways = 6
`*`5
`*`4
`*`3 = 360