Question

At a game show, there are 8 people (including you and your friend) in the

front row.
The host randomly chooses 3 people from the front row to be contestants.
The order in which they are chosen does not matter.
How many ways can you and your friend both be chosen?

Answer 1

6

Explanation:

For both to be chosen the other spot can be taken by any of the other 6 people in the row. So six possibilities

Answer 2

A.
`^6C_1=6`

Explanation:

Given,

The total number of people = 8,

The number of people have to chosen = 3,

Since, me and my friend both have to be chosen,

So, the remaining number of people = 8 - 2 = 6,

And, the number of remaining number of people have to be chosen = 3 - 2 = 1

Also, the order does not matter,

Hence, the total way of choosing = Total combination of me and my friend × total combination of choosing 1 person out of 6 people

`=^2C_2* ^6C_1`

`=1* ^6C_1`

`=6`

Option A is correct.