Question

You are planning a party. The space restriction is such that you can only invite 4 people. There are 9 friends to choose from. In how many ways can you select those 4 people?

a. There are (9-8+7+6(4+3+2+1) many ways.
b. There are (9-4)*(8-3)*(7-2)*(6-1) many ways.
c. There are 9*8*7*6 many ways.
d. There are 9*8*7*6/4*4*3*2*1) many ways.

Answer 1

Given:

Total number of friends = 9

Number of friend to invite = 4

To find:

The number of ways.

Solution:

We know that, total number of ways to select r items from n items is

`^nC_r=(n!)/(r!(n-r)!)`

So, the total number of ways to select 4 people from 9 friends is

`^9C_4=(9!)/(4!(9-4)!)`

`^9C_4=(9!)/(4!5!)`

`^9C_4=(9* 8* 7* 6* 5!)/(4* 3* 2* 1* 5!)`

`^9C_4=(9* 8* 7* 6)/(4* 3* 2* 1)`

Therefore, the required number of ways is
`(9* 8* 7* 6)/(4* 3* 2* 1)`.

Note: All options are incorrect.