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Question

# Four numbers are chosen at random from {1,2,3,......,40}. The probability that they are not consecutive is

A
12470
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B
47969
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C
24692470
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D
79657969
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Solution

## The correct option is C 24692470Probability when all four chosen numbers are not consecutive = 1 − Probability when all four chosen numbers are consecutiveNumber of cases when all selected numbers are consecutive =37 [(1,2,3,4);(2,3,4,5);........(37,38,39,40)]Total number of cases of selecting four numbers out of 40 =40C4Probability when all four chosen numbers are consecutive =3740C4=12470Probability when all four chosen numbers are not consecutive =1−12470=24692470

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