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  • What is the probability that a divisor of is a multiple of  <img alt="10^{96}" src="https://entranceco

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

Option: 1

\frac{1}{625}


Option: 2

\frac{4}{625}


Option: 3

\frac{12}{625}


Option: 4

\frac{16}{625}


Answers (1)

best_answer

\because                10^{99}=2^{99} \times 5^{99}

So Number of factors of 110^{99}=(99+1)(99+1)=10^{4}

Again we have 10^{99}=10^{96} \times 10^3=10^{96} \times 2^3 \times 5^3

So factors of 10^{99} which are multiple of 10^{96}=\left ( 3+1 \right )\left ( 3+1 \right )=16

So Req. prob =\frac{\text{fav.factors}}{\text{Total factor}}=\frac{16}{10^{4}}

Posted by

Rishabh

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