Q. Four numbers are chosen at random from {1,2,3,…,40}. The probability that they are not consecutive, is
A) $\frac{1}{2470}$
B) $\frac{4}{7969}$
C) $\frac{2469}{2470}$
D) $\frac{7965}{7969}$
Explanation
(c)
Probability that four of the numbers are consecutive
$= \frac{\ ^{37}C_{1}}{\ ^{40}C_{4}}$
Now, probability that four of the numbers are not consecutive
$= 1 - \frac{\ ^{37}C_{1}}{\ ^{40}C_{4}} = 1 - \frac{37}{91390} = \frac{2469}{2470}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.