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  4. The total number of six digit numbers, formed using the digits 4,5,9 only and divisible by 6 , is

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Q. The total number of six digit numbers, formed using the digits $4,5,9$ only and divisible by 6 , is __

JEE MainJEE Main 2023Permutations and Combinations

Solution:

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Taking three digit
$ 4,5,9,4,4,4 \Rightarrow \frac{5 !}{3 !}=20$
$ 4,5,9,5,5,5 \Rightarrow \frac{5 !}{4 !}=5 $
$4,5,9,9,9,9 \Rightarrow \frac{5 !}{4 !}=5$
$ 4,5,9,4,5,9 \Rightarrow \frac{5 !}{2 ! 2 !}=30 $
$ \text { Total }=81$