JEE Main 2023 (Online) 29th January Morning ShiftQuestion 1
If all the six digit numbers $x_1x_2x_3x_4x_5x_6$ with $0<x_1<x_2<x_3<x_4<x_5<x_6$ are arranged in the increasing order, then the sum of the digits in the $72^{\text{th}}$ number is ______.
Permutation and Combination
Answer$32$
Solution
There are $\binom96=84$ such numbers; $\binom85=56$ start with $1$ and $\binom64=15$ start with $23$, so the $72$nd is the first starting with $24$: $245678$, digit sum $32$.