Question

Three distinct numbers are chosen randomly from the first 50 natural numbers. Find the probability that all the three numbers are divisible by both 2 and 3.

Answer 1

S = {1, 2, 3 ........ 50}

n(S) = 50

E = [no’s divisible by 2 and 3]

E = [6, 12, 18, 24, 30, 36, 42, 48]

n(E) = 8

Probability that all the three numbers are divisible by both 2 and 3.

P(E) = `(""^8"C"_3)/(""^50"C"_3)`

\[\begin{aligned}
& =\frac{\frac{|\underline{8}}{|\underline{3}|\underline{5}}}{\frac{|\underline{50}}{|\underline{3}|\underline{47}}} \\
\end{aligned}\]

= `(8 xx 7 xx 6)/(50 xx 49 xx 48)`

= `1/350`