The crew of an 8 member rowing team is to be chosen from 12 men, of which 3 must row on one side only and 2 must row on the other side only. Find the number of ways of arranging the crew with 4 members on each side.
a)40320
b)60480
c) none of above.
My analogy – I tried creating all possible ways 8 people could be selected from 3 groups ( A- 7 people ,B -2 people ,C- 3 people )i.e
7 from A , 1 from B +
7 from A , 1 from C +
6 from A , 2 from B +
6 from A , 2 from c +
6 from A , 1 from B , 1 from C +
.
.
.
But this is getting too long.. any thoughts on a simpler method ?
Best Answer
First allot the "special" 3 for 1 side & "special" 2 for the other.
The 7 men left can be allotted in ${7\choose 1}{6\choose 2}$ = 105 ways
Now permute them to get ans = $105\cdot4!\cdot4!$ = 60,480 ways