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Among the 8! permutations of the digits 1,2,3,.....8, consider those arrangements which have the following property:if you take any 5 consecutive positions , the product of the digits in those positions is divisible by 5.find the number of such arrangements?

Among the 8! permutations of the digits 1,2,3,.....8, consider those arrangements which have the following property:if you take any 5 consecutive positions , the product of the digits in those positions is divisible by 5.find the number of such arrangements?


 


 

Grade:11

1 Answers

mycroft holmes
272 Points
10 years ago

Its obvious that the number 5 has to be in the 4th position or 5th position. The number of possible arrangements is therefore 7! X 2.

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