Claudia is arranging seating for her sorority's fall banquet. She has to sit 7 seniors, 5 juniors, 9 sophomores and 3 freshmen at the end banquet table. What is the probability members of the same class will all sit together?

7!x5!x9!x3!= 1.317x10^12
Am I correct?

1 answer

first of all, they asked for a probability.

How many ways to seat all the people?

Now, consider all the members of a class as one person. How many ways to seat them now?

Do the same for the other classes.

(Total ways to seat fused classes) divided by (total ways to seat everyone) is the probability.