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

Question

Four numbers are chosen at random from 1,2,3, ldots, 40 . The probability that they are not consecutive, is (A) (1/2470) (B) (4/7969) (C) (2469/2470) (D) (7965/7969)

Tardigrade Admin · Accepted Answer

Probability that four of the numbers are consecutive =(37/40) 37 C1 Now, probability that four of the numbers are not consecutive =1-(37/40)C4 =(2469/2470)

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

$\frac{1}{2470}$

$\frac{4}{7969}$

$\frac{2469}{2470}$

$\frac{7965}{7969}$

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

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

24701​

79694​

24702469​

79697965​