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Three numbers are chosen from 1 to 20. F...

Three numbers are chosen from 1 to 20. Find the probability that they are consecutive.

A

` ( 7 ) / (190) `

B

` ( 3 )/( 190) `

C

` (5 ) /(190 ) `

D

` (1 )/(3) `

Text Solution

Verified by Experts

The correct Answer is:
B
Number of sample space for selecting three numbers between 1 to 20 ` = ""^ (20 ) C_ 3 `
Number of ways that they are consecutive numbers = 18
` therefore ` Required probability
` = ( 18) / (""^(20) C _ 3 ) = ( 18 xx 3 xx 2 ) /( 20 xx 19 xx 18 ) `
` = ( 3 )/( 190 ) `
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