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標題:
Permutation and Combination
發問:
Mr and Mrs Fung invite 10 friends to their house warming party.a) (i) When their friends arrive, Mr and Mrs Fung shake hand with each of them. How many hand-shakings are there?a) (II) If everyone in the house shakes hand with each other, how many hand-shakings are there?b) By the end of the party, they take a... 顯示更多 Mr and Mrs Fung invite 10 friends to their house warming party. a) (i) When their friends arrive, Mr and Mrs Fung shake hand with each of them. How many hand-shakings are there? a) (II) If everyone in the house shakes hand with each other, how many hand-shakings are there? b) By the end of the party, they take a photo. They are arranged in 2 rows of 6, find the number of possible arrangements if (i) Mr and Mrs Fung stand in different rows (ii) Mr and Mrs Fung stand next to each other
最佳解答:
a(i) 2*10 =20 a(ii) 12C2=12*11/2 =66 b(1) Mr F v 1v 2 v 3 v 4 v 5 v <- 6 arrangements for 1st row Mrs F v 1v 2 v 3 v 4 v 5 v <-6 arrangements for 2nd row =10! * (6^2) *2 (the row that Mr Fung & Mrs Fung stand can be exchanged, so 乘 2) =261,273,600 // b(II) =10! *9 =32,659,200 // 2011-12-24 22:27:36 補充： sorry, correction: b(ii) Mr Fung & Mrs Fung stand next to each other , so treat it as 1 unit, so total 11 units v 1 v 2 v 3 v 4 v 5 v 6 v 7 v 8 v 9 v 10 v 11 v v 6 v , this one should be cancelled, since they will be separated into 2 different rows =10! *10 =36,288,000// 2011-12-25 17:02:06 補充： sorry, 再要correction b(ii) 10!*10*2 (因為mr. & mrs. can exchange the positions, 所以乘 2) =72,576,000 //
其他解答:
Permutation and Combination
發問:
Mr and Mrs Fung invite 10 friends to their house warming party.a) (i) When their friends arrive, Mr and Mrs Fung shake hand with each of them. How many hand-shakings are there?a) (II) If everyone in the house shakes hand with each other, how many hand-shakings are there?b) By the end of the party, they take a... 顯示更多 Mr and Mrs Fung invite 10 friends to their house warming party. a) (i) When their friends arrive, Mr and Mrs Fung shake hand with each of them. How many hand-shakings are there? a) (II) If everyone in the house shakes hand with each other, how many hand-shakings are there? b) By the end of the party, they take a photo. They are arranged in 2 rows of 6, find the number of possible arrangements if (i) Mr and Mrs Fung stand in different rows (ii) Mr and Mrs Fung stand next to each other
最佳解答:
a(i) 2*10 =20 a(ii) 12C2=12*11/2 =66 b(1) Mr F v 1v 2 v 3 v 4 v 5 v <- 6 arrangements for 1st row Mrs F v 1v 2 v 3 v 4 v 5 v <-6 arrangements for 2nd row =10! * (6^2) *2 (the row that Mr Fung & Mrs Fung stand can be exchanged, so 乘 2) =261,273,600 // b(II) =10! *9 =32,659,200 // 2011-12-24 22:27:36 補充： sorry, correction: b(ii) Mr Fung & Mrs Fung stand next to each other , so treat it as 1 unit, so total 11 units v 1 v 2 v 3 v 4 v 5 v 6 v 7 v 8 v 9 v 10 v 11 v v 6 v , this one should be cancelled, since they will be separated into 2 different rows =10! *10 =36,288,000// 2011-12-25 17:02:06 補充： sorry, 再要correction b(ii) 10!*10*2 (因為mr. & mrs. can exchange the positions, 所以乘 2) =72,576,000 //
其他解答:
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