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Q. The number of seven digits odd numbers, that can be formed using all the seven digits $1,2,2,2,3,3,5$ is_______

JEE MainJEE Main 2023Permutations and Combinations

Solution:

Digits are $1,2,2,2,3,3,5$
If unit digit 5 , then total numbers $=\frac{6 !}{3 ! 2 !}$
If unit digit 3 , then total numbers $=\frac{6 !}{3 !}$
If unit digit 1 , then total numbers $=\frac{6 !}{3 ! 2 !}$
$\therefore$ total numbers $=60+60+120=240$