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Standard XII

Mathematics

Combination of Atleast One Thing from n Things When All Are Not Different

The number of...

Question

The number of ways in which we can arrange the digits 1, 2, 3....9 such that the product of five digits at any of the five consecutive positions is divisible by 7 is:

7!

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^{9} P_{7}

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8!

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5 (7!)

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Solution

The correct option is A $8!$
Total number of ways such that any of five consecutive positions is divisible by 7 is such that 7 should be in the middle.
$∴$ Total number of ways are number of ways of filling the eight left places; i.e. 8!

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The number of ways in which we can arrange the digits 1, 2, 3....9 such that the product of five digits at any of the five consecutive positions is divisible by 7 is:

The correct option is A 8!Total number of ways such that any of five consecutive positions is divisible by 7 is such that 7 should be in the middle.∴ Total number of ways are number of ways of filling the eight left places; i.e. 8!

The correct option is A $8!$
Total number of ways such that any of five consecutive positions is divisible by 7 is such that 7 should be in the middle.
$∴$ Total number of ways are number of ways of filling the eight left places; i.e. 8!