a team of 8 players is to be selected from a group of 12 players, followed by choosing a captain & a vice-captain from the 8 selected. In how many ways can this be done?(ans.27720)hint:use combinations.
2006-10-21 21:37:02 · 3 answers · asked by amrita b 1 in Science & Mathematics ➔ Mathematics
(12c8) * (8c2) * 2 =
(12*11*10*9 / (4*3*2*1)) * (8*7 / (2*1)) * 2 =
495 * 28 * 2 =
27,720
The last multiply by 2 is because a captain and vice captain chosen from the 8 depends on the order they are selected. (If the question had been to select 2 co-captains from the 8, the answer would have been 495*28 = 13,860.)
2006-10-21 21:44:50 · answer #1 · answered by Joe C 3 · 2⤊ 0⤋
Joe C is right, but I would break it into 2 separate operations for clarity.
Choose 8 players out of 12: (12 C 8) = 12!/(8!4!) = 495
Choose a captain and vice captain from a team of 8: 8*7 = 56
495*56 = 27720
2006-10-22 05:06:11 · answer #2 · answered by sofarsogood 5 · 0⤊ 0⤋
mCn = mC(m-n) = m!/n!(m-n)!
(12C8)*8*7 =
12*11*10*9*8*7
------------------- = 27720
1*2*3*4
(495 possible teams)(8 possible captains)(7 possible vice-captains)
2006-10-22 05:07:52 · answer #3 · answered by Helmut 7 · 0⤊ 0⤋