First slide

Combinations

Question

Two numbers are selected at random from a set of first 120 natural numbers, then the probability that product of selected number is divisible by 3 is

Moderate

A

$\frac{13}{357}$
B

$\frac{199}{357}$
C

$\frac{158}{357}$
D

$\frac{160}{357}$

Solution

$\begin{array}{l} {3, 6, 9, - - -, 120} \\ {1, 2, 4, 5, - - -, 119} \\ P (A) = \frac{40_{C_{2}} + 80_{C_{1}} \times 40_{C_{1}}}{120_{C_{2}}} \\ = \frac{199}{357} \end{array}$

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