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Question

The number of ways in which the letters of the word ARRANGE can be arranged such that both R do not come together is?


A

360

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B

900

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C

1260

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D

1620

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Solution

The correct option is B

900


Explanation for the correct option:

Find the number of ways

Consider the given word ARRANGE

In the above word A is repeated two times, R is repeated two times, N, G and E are present in only one time.

The total number of possible arrangements can be expressed as,

7!2!×2!=7×6×5×4×3×2!2×1×2!=1260

Number of arrangements when two R comes together can be expressed as,

6!2!=6×5×4×3×2!2!=360

Thus, the final answer for the number of ways which R does not come together can be expressed as,

1260-360=900

Hence, the correct answer is Option B.


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