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

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

EAMCETEAMCET 2007

Solution:

Probability that four of the numbers are consecutive
$=\frac{37}{40}{ }^{37} C_{1}$
Now, probability that four of the numbers are
not consecutive $=1-\frac{37}{40}_{C_{4}}$
$=\frac{2469}{2470}$