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The number of positive six-digit integer...

The number of positive six-digit integers which are divisible by `9` and four of its digits are `1`, `0`, `0`, `5` is

A

`60`

B

`120`

C

`180`

D

`210`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` The sum of digits must be divisible by `9`
The pair of missing numbers must be `(1,2)` or `(0,3)`
Case I : `(1,2)`
`implies` when `1` is first digit the remaining digits `(1,2,0,0,5)` can be arranged in `60` days, when `5` or `2` is first digit then in `30` ways each
Case II : `(0,3)` will have `3xx20=60` ways
So total number of ways `=60+2xx30+3xx20=180`
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