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Q.

Among the 8! permutations of the digits 1, 2, 3, ..., 8, consider those arrangements which have the following property. If we take any five consecutive positions, the product of the digits in these positions is divisible by 5. The number of such arrangements is equal to

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a

7!

b

2.(7!)

c

7C4

d

none of these

answer is B.

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Detailed Solution

Let the arrangement be x1    x2    x3    x4    x5    x6    x7    x8. Clearly 5 should occupy the position x4 or x5. Thus, required number of arrangements is 2(7!).
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Among the 8! permutations of the digits 1, 2, 3, ..., 8, consider those arrangements which have the following property. If we take any five consecutive positions, the product of the digits in these positions is divisible by 5. The number of such arrangements is equal to