F.5 Permutation&Combination4
2010-12-28 8:40 pm
The coach of a school athletic team is going to select 4 players for a 4x100m relay race from n members of the team. It is given that Franky must be selected, but the leg of the race he is responsible for has not yet been determined. If the coach has 2016 ways to arrange the legs of the race, find the value of n.
回答 (2)
2010-12-28 9:13 pm
✔ 最佳答案
Thecoach of a school athletic team is going to select 4 players for a 4x100m relayrace from n members of the team．It isgiven that Franky must be selected，but the leg of the
race he is responsible for has not yet been determined．If the coach has 2016 ways to
arrange the legs of the race，find the value of n.
Sol
4－1=3
4!=24
2016/24=84
C(n，3)=n!/[n－3)!3!]==n(n－1)(n－2)/6=84
n(n－1)(n－2)=6*84=504
8*7*6=336
9*8*7=504
So
n=9
2010-12-28 9:29 pm
(n-1)C3 = 84
(n - 1)(n - 2)(n - 3) = 504
n^3 - 6n^2 + 11n - 510 = 0
(n - 10)(n^2 + 4n + 51) = 0
n = 10 or no solution
(n - 1)(n - 2)(n - 3) = 504
n^3 - 6n^2 + 11n - 510 = 0
(n - 10)(n^2 + 4n + 51) = 0
n = 10 or no solution
收錄日期: 2021-04-13 17:43:37
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