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Question

Three numbers are chosen from 1 to 20. The probability that they are not consecutive is


A

186190

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B

187190

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C

188190

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D

1820C3

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Solution

The correct option is B

187190


Number of ways to choose three numbers from 1 to 20 = 20C3=1140

Now, the set of three consecutive numbers from 1 to 20 are (1, 2, 3), (2, 3, 4), (3, 4, 5), ..........., (18, 19, 20).

So, the number of ways to choose three numbers from 1 to 20 such that they are consecutive is 18.

P(three numbers choosen are consecutive)

Number of ways to choose three

=consecutive number from 1 to 20Number of ways to choose three

numbers from 1 to 20

=1820C3=181140=3190

P(three numbers choosen are not consecutive) = 1 - P(three numbers choosen are consecutive)

=13190=187190

Hence, the correct answer is option (b).


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