JEE Main 2022 (Online) 26th July Morning ShiftQuestion 1
The number of $5$-digit natural numbers, such that the product of their digits is $36$, is ________.
Permutation and Combination
Answer$180$
Solution
Digits with product 36 from $\{1,2,3,4,6,9\}$, five digits. Multisets: $\{1,1,1,4,9\}$: $5!/3!=20$; $\{1,1,1,6,6\}$: $10$; $\{1,1,2,3,6\}$: $5!/2!=60$; $\{1,1,2,2,9\}$: $30$; $\{1,1,3,3,4\}$: $30$; $\{1,2,2,3,3\}$: $30$. Total $=20+10+60+30+30+30=180$.