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Q.
If three distinct numbers are chosen randomly from the first $100$ natural numbers, then the probability that all three of them are divisible by both $2$ and $3$ is
Probability
Solution:
If a number is to be divisible by both $2$ and $3$ , it should be divisible by their L.C.M. L.C.M. of $2$ and $3$ is $6$ . The numbers are $6,12,18, \ldots, 96$. The total number is $16$ . Hence; the probability is
$\frac{{ }^{16} C_{3}}{{ }^{100} C_{3}}=\frac{4}{1155}$