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Question

If n integers taken at random are multiplied together, then the probability that the last digit of the product is 1,3,7 or 9 is

A
2n5n
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B
4n2n5n
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C
4n5n
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D
None of these
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Solution

The correct option is A 2n5n
In any number the last digits can be 0,1,2,3,4,5,6,7,8,9.
Therefore last digit of each number can be chosen in 10 ways.
Thus, exhaustive number of ways =10n.
If the last digit be 1,3,7 or 9 none of the number can be even or end in 0 or 5.
Thus, we have a choice of 4 digits 1,3,7 or 9 with which each of n numbers sholud end.
So, favorable number of ways =4n.
Hence, the required probability =4n10n=2n5n

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