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Given are six 0's, five 1's and four 2'...

Given are six `0'`s, five `1'`s and four `2's` . Consider all possible permutations of all these numbers. [A permutations can have its leading digit `0`].
How many permutations have the first `0` preceding the first `1` ?

A

`"^(15)C_(4)xx^(10)C_(5)`

B

`"^(15)C_(5)xx^(10)C_(4)`

C

`"^(15)C_(6)xx^(10)C_(5)`

D

`"^(15)C_(5)xx^(10)C_(5)`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` The no. of ways of arranging `2'` is `.^(15)C_(4)`.
Fill the first empty position left after arranging the `2's` with a `0`(`1` way) an pick the remaining five places from the position of reamining five zeros `.^(10)C_(5)` ways.
`:. ^(15)C_(4)xx1xx^(10)C_(5)`
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