First slide

Introduction to probability

Question

Three integers are chosen at random from the set of first 20 natural numbers. The chance that their product is a multiple of 3 is

Moderate

A

$\frac{194}{285}$
B

$\frac{1}{57}$
C

$\frac{13}{19}$
D

$\frac{3}{4}$

Solution

The total number of ways of selecting 3 integers from 20 natural numbers is ²⁰C₃ = 1140.
Their product is a multiple of 3 means at least one number is divisible by 3.
The numbers which are divisible by 3 are 3, 6, 9, 12, 15, l8 and
the number of ways of selectin g at least one of them is $^{6} C_{1} \times^{14} C_{2} +^{6} C_{2} \times^{14} C_{1} +^{6} C_{3} = 776$ .
Hence, the required probability is 776/1140 = 194/285.

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