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Question

If n positive integers are taken at random and multiplied together, then the probability that the last digit of the product is 2,4,6or 8, is


A

(4n+2n)5n

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B

(4nx2n)5n

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C

(4n-2n)5n

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D

None of these

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Solution

The correct option is C

(4n-2n)5n


Explanation for correct option

We know that,

Probability of an event is =numberoffavorableoutcomestotalnumberofoutcomes

Therefore the probability of integer ending in 1,2,3,4,6,7,8,9 is 810=45

Hence, the probability that the last digit of the product of n integers is 45n

The probability that the last digit of the product of n integers ends with 1,3,7, and 9 is 25n

Hence, the required probability=45n25n

=4n2n5n

Hence, option (C) is correct.


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