Q87 / 150 · MHT CET 2024 (02 May Shift 2) · Mathematics

Number of different nine digit numbers, that can be formed from the digits in the number 223355888 by rearranging its digits, so that the odd digits occupy even positions, is

A
16
B
40
Correct answer
C
60
D
180

Solution

Since $3,3,5$, 5, i.e., odd digits occupy even positions and $2,2,8,8,8$ occupy remaining 5 odd places. $\begin{aligned} \therefore \quad \text { Required number of ways } & =\frac{4!}{2!2!} \cdot \frac{5!}{2!3!} \\ & =6 \times 10=60 \end{aligned}$

Hence, the correct answer is option: 'C'.

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