All possible numbers are formed using the digits 1 , 1 , 2 , 2 , 2 , 2 , 3 , 4 , 4 taken all at a time. The…

1. $175$
2. $162$
3. $180$
4. $160$

Solution

Odd digits: $1, 1, 3$
Even digits: $2, 2, 2, 2, 4, 4$
The number of ways of placing odd digits at even position $= {}^{4}C_3\times \frac{3!}{2!}=4\times 3=12$
The number of ways of placing even digits $=\frac{6!}{4! 2!}=15$
$\therefore$ Total number of ways $=12\times 15=180$

Asked in: JEE Main 2019 (08 Apr Shift 1)

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