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Find the total number of nine-digit numb...

Find the total number of nine-digit numbers that can be formed using the digits 2, 2, 3, 3, 5, 5, 8, 8, 8 so that the odd digit occupy the even places.

A

16

B

36

C

60

D

180

Text Solution

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The correct Answer is:
C
`X-X-X-X-X.` The four digits 3, 3, 5, 5 can be arranged at `(-)` places in `(4!)/(2!2!) = 6` ways.
The five digits 2, 2, 8, 8, 8 can be arranged at (X) palces in `(5!)/(2!3!)` ways = 10 ways.
Total number of arrangements `= 6 xx 10 = 60`
[since, events A and B are independent, therefore `A nn B = A xx B`]
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