JEE Main 2020 (Online) 6th September Morning ShiftQuestion 1
Out of $11$ consecutive natural numbers if three numbers are selected at random (without repetition), then the probability that they are in A.P. with positive common difference, is :
Probability
Solution
For common difference $d$ there are $11-2d$ triples ($d=1,\ldots,5$): $9+7+5+3+1=25$. Probability $=\frac{25}{\binom{11}3}=\frac{25}{165}=\frac5{33}$.