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in how many ways the letters of the word 'Arrange' can be arranged so that 2A's are separated by exactly 2 letters

in how many ways the letters of the word 'Arrange' can be arranged  so that 2A's are separated by exactly 2 letters

Grade:12

2 Answers

Shaswata Biswas
132 Points
7 years ago
If we see the case, you can shift the 2 A`s upto 4 places from the left. For each case, the other 4 letters can be arranged in their places in 4! Ways. And the 2 A`s can arrange in 2! Ways within themselves.So, for 4 such cases the total no. of arrangement is 4*4!2! = 192 ways.
Shaswata Biswas
132 Points
7 years ago
Sorry, my mistake. There are 5 letters remaining. Then the correct no. of permutations is 4*5! = 480. The case of 2! Is not applicable as both are same letters.

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