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Question

Let A be the set of all permutations a1,a2,....,a6 of 1,2,...,6 such that a1,a2,....ak is not a permutation of 1,2,...,k for any k,1k5. Then the number of elements in A is

A
192
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B
408
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C
312
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D
528
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Solution

The correct option is D 528
Since ak does not have k element as a permutation, it has 5 elements each with 2 possibilities (one of being in the permutation and the other of not being the permutation). Hence, total permutations possible are 6! 6C1×25=528

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