JEE Main 2026 (Online) 23rd January Evening ShiftQuestion 1
Let $S$ denote the set of $4$-digit numbers $abcd$ such that $a>b>c>d$ and $P$ denote the set of $5$-digit numbers having product of its digits equal to $20$. Then $n(S)+n(P)$ is equal to $\_\_\_\_\_\_$ .
Permutation and Combination
Answer$260$
Solution
$n(S)=\binom{10}{4}=210$. Digit products $20$: $\{4,5,1,1,1\}$ gives $20$ numbers, $\{2,2,5,1,1\}$ gives $30$; $n(P)=50$. Total $260$.