First slide

Permutations

Question

How many different nine digit numbers can be formed from the number 223355888 by rearranging its digits so that the odd digits occupy even positions?

Moderate

A

16
B

36
C

60
D

180

Solution

The four digits 3, 3, 5, 5 can be arranged at four even places in $\frac{4!}{2! 2!} = 6$ ways and the remaining digits viz., 2, 2, 8, 8, 8 can be arranged at the five odd places in $\frac{5!}{2! 3!} = 10$ ways.
Thus, the number of possible arrangements is (6) (10) = 60.

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