Question

Six married couple are sitting in a room. Find the number of ways in which $4$ people can be selected.

• A. 480
• B. 200
• C. 898
• D. 100

Answer 1

The correct option is A 480

Solution:

A couple is a group of two people (assuming they are all married)

We know that:

1. There are twelve people in total

Now, out of the four people, two have to form a couple.

This leaves us with $10$ people that can fill the rest.

Out of the two we can pick out, the first can be any out of the $10$.

The second person can't be the selected person's husband/wife.

This leaves us $8$ people for the second choice.

There are $10\times 8$ or $80$ choices for one couple

Since there are six couples, we multiply $6$ by $80$

$6\times 8=480$ ways