Question

In how many ways can 12 boys be seated on two benches x, y such that 6 boys sit on each bench and two of them A,B are to sit on bench x and C,D on the bench y

• A. ${}^8{C}_{4}6!6!$
• B. ${}^8{C}_{6}6!6!$
• C. $6!6!$
• D. ${}^8{C}_{4}6!$

Answer 1

The correct option is A ${}^8{C}_{4}6!6!$

Out of 12 boys, four of them A,B,C and D already chosen out then out of remaining 8 boys, we need to select 4 boys for each bench ie $8_{C_4}$ and there will arrangement of 6 boys on each bench
So required number of ways $8_{C_4}\times 6!\times 6!$