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Q.
The total number of $5$-digit numbers, formed by using the digits $1,2,3,5,6,7$ without repetition, which are multiple of $6$, is
JEE MainJEE Main 2022Permutations and Combinations
Solution:
To make a no. divisible by $3$ we can use the digits
$1,2,5,6,7$ or $1,2,3,5,7$
Using $1,2,5,6,7$, number of even numbers is
$=4 \times 3 \times 2 \times 1 \times 2=48$
Using $1,2,3,5,7$, number of even numbers is
$=4 \times 3 \times 2 \times 1 \times 1=24$
Required answer is $72$.