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.