Question

​students: Ann comma Bob comma Carol comma Dan comma Eve comma and Frank​, are randomly lined up for a picture. What is the probability that Carol and Dan are standing next to each other​ (in either​ order)?

Answer 1

Answer:

0.1667

Step-by-step explanation:

The total number of ways these 6 people could stand in a row: 6!

This means 6 * 5 * 4 * 3 * 2 * 1

Thus the total number of ways they can stand together is 720.

If we consider Carol and Dan to be one person, as they are always standing together, we can solve this question fairly easily. Now there are only 5 people total. This includes Ann, Bob, Eva and Frank as 4 people. The last person is Carol and Dan together.

The number of ways 5 people could arrange themselves: 5!

This equals: 120

Probability = Number of ways to stand with Carol and Dan together / Total number of ways to stand

Probability = 120 / 720

Probability = 0.1667