Question

10 chairs are arranged in a row and are numbered 1 to 10. 4 men have to be seated in these chairs so that the ending chairs in the row can never be empty. In how many ways can this be done?

• A. 672
• B. 336
• C. 112
• D. 168

Answer 1

The correct option is A

672

First select any two men from the four and arrange them in the ending seats in ${}^4{C}_2$*2!

Then select two seats out of the 8 seats and arrange the two men in that. The number of ways that this can be done is ${}^8{C}_2$*2!

So, the total number of ways in which this can be done is ${}^8{C}_2$*2! *${}^4{C}_2$*2! = 672