Question

The crew of an 8 oar boat is to be choosen from twelve Men, of whom 3 can row on stroke side only. The number of ways the crew can be arranged is

• A. ${}^9{C}_4{.}^8{C}_4$
• B. ${}^9{C}_4{.}^8{C}_{4}4!4!$
• C. ${}^{12}{C}_8{.}^9{C}_{4}4!4!$
• D. ${}^{12}{C}_4{.}^8{C}_{4}4!4!$

Answer 1

Answer: (B)

${}^9{C}_4{.}^8{C}_{4}4!4!$

We are to choose 4 persons for each side. As 3 persons can row only on the stroke side, therefore the number of ways in which we can choose 4 persons for non-stroke side is ${9_C}_4$. Having done this,we are left with 8 persons .So, we can choose 4 persons for stroke side in ${8_C}_4$
$\therefore$The required number of arrangements $={9_C}_4\times {8_C}_4\times 4!\times 4!$