Question

What is the probability that divisor of 10^99 is a multiple of 10^96

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

As 10⁹⁹=2⁹⁹⋅5⁹⁹,

using divisor function 1,2, the number of divisors is (1+99)(1+99)

which are the product of

{1,2¹,⋯,2⁹⁸,2⁹⁹} and {1,5¹,⋯,5⁹⁸,5⁹⁹}

To be multiple of 10⁹⁶ we need to take

{2⁹⁶,2⁹⁷,2⁹⁸,2⁹⁹} and {5⁹⁶,5⁹⁷,5⁹⁸,5⁹⁹}

i.e., there are 4⋅4=16 of them

So, the required probability is

4²/100²=1/625

Hope it helps.....

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