Question

Five people are to be chosen from a group of 20 to take a trip. In how many ways can this be done if A and B refuse to travel without each other

Answer 1

Explanation:

If A and B refuse to travel without each other, then we can treat them as a single unit. So, we only need to choose 4 people from the remaining 18. The total number of ways to do this is:

${18 \choose 4} = \frac{18!}{4!14!} = 3060$

Therefore, there are 3060 ways to choose 5 people from a group of 20 if A and B refuse to travel without each other.