A program consists of 4 musical numbers and 3 speeches In ho

A program consists of 4 musical numbers and 3 speeches. In how many ways can the program be arranged so that it begins and ends with a musical number?

Solution

There are 4 musical numbers and 3 speeches

AS begin and end musical numbers 2 musical numbers selected from 4 and put in the ends

This can be done in 2(4C2) = 12 ways

The remaining are 2 musical and 3 speeches. This can be arranged in 5! ways

Hence total no of ways = 12 (5!) = 1440