Permutation and Combination

[匿名]

2010-05-30 8:54 pm

Find the number of 4 letters word that can be formed from the word MATHEMATICS.

更新1:

To 001 : Since any 4 letters selected can be arranged differently, so this question is also a permutation problem, please clarify.

回答 (1)

用戶2053

2010-05-30 9:14 pm

✔ 最佳答案

MM AA TT HEICS
When the 4 letters word have no repeat letters :
i.e. (any 4 from M A T HEICS)
8C4 * 4! = 1680 cases
When the 4 letters word have a pair of repeat letters :
i.e. (MM or AA or T T + any 2 from AT HEICS or MT HEICS or MA HEICS)
(3 * 7C2) * 4! / 2! = 756 cases
When the 4 letters word have two pair of repeat letters :
i.e. (MM+AA or MM+TT or AA+TT)
3 * 4! / ( 2! 2!) = 18 cases
Total : 1680 + 756 + 18 = 2454 words can be form.

2010-05-30 16:00:20 補充：
My answer considered this question is a permutation problem.

2010-05-30 16:01:17 補充：
8C4 * 4! = 8P4

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