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Mathematics
If the letters of the word PROBABILITY are arranged at random,find the number if arrangements that the two B's are separated.
1 個解答
評分
- 翻雷滾天 風卷殘雲Lv 710 年前最佳解答
No. of all possible arrangements = 11!/(2! x 2!) = 9979200
since in 11 letters, there are 2 B's and 2 I's
Instead, we can count the no. of arrangements that 2 B's are together, i.e. we can treat it as if there were 10 letters in which 2 are the same (the 2 I's)
So no. of poss. arrangements that 2 B's are together is:
10!/2! = 1814400
Hence no. of possible arrangements that the B's are separated is:
9979200 - 1814400 = 8164800
參考資料： 原創答案
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