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? [2000]

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? [2000]

Smart Achievers · Accepted Answer

(3)

$X - X - X - X - X .$ $The four digits 3, 3, 5, 5 can be arranged at (-) places in$

$\frac{4!}{2! 2!} = 6 ways$

$The five digits 2, 2, 8, 8, 8 can be arranged at (X) places in$

$\frac{5!}{3! 2!} = 10 ways$

$∴$ $Total number of arrangements = 6 \times 10 = 60 ways$

Solution

Q.
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 [2000]

1 16

2 36

3 60

4 180

Ans.
(3)

$X - X - X - X - X .$ $The four digits 3, 3, 5, 5 can be arranged at (-) places in$

$\frac{4!}{2! 2!} = 6 ways$

$The five digits 2, 2, 8, 8, 8 can be arranged at (X) places in$

$\frac{5!}{3! 2!} = 10 ways$

$∴$ $Total number of arrangements = 6 \times 10 = 60 ways$

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