Three integers are chosen at random from the first 20 integers. T… - Vidyadip

MCQ

Three integers are chosen at random from the first 20 integers. The probability that their product is even is:

A
$\frac{2}{19}$
B
$\frac{3}{29}$
✓
$\frac{17}{19}$
D
$\frac{4}{19}$

✓

Answer

Correct option: C.

$\frac{17}{19}$

Number of ways in which we can choose three distinct integers from 20 integers $\ ^{20}\text{C}_3=1140$
We know that, if we take three odd numbers, there product will always be an odd number.
Out of 20 consecutive integers, 10 are even and 10 are odd integers.
Number of ways in which we can choose three distinct odd integers from 10 odd integers $=\ ^{10}\text{C} _3=120$
P(product is even) = 1 - P(product is odd),
$=1-\frac{120}{1140}=\frac{1140-120}{1140}=\frac{1020}{1140}=\frac{17}{19}$

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