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How many positive divisors does 4000 = 2^5 5^3 have?

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How many positive divisors does 4000 = 2^5 5^3 have?

(a) 49

(b) 73

(c) 65

(d) 15

The question was asked in exam.

My question comes from Multiplication Theorem on Probability topic in portion Discrete Probability of Discrete Mathematics

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Correct choice is (d) 15

Explanation: Any positive divisor of 4000 must be of the form 2^x5^y, where x and y are integers satisfying o<=x<=5 and 0<=y<=3. There are 5 possibilities for x and 3 possibilities for y and hence there are 3*5 = 15(rule of product) positive divisors of 4000.

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