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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`].
In how many permutations does the first `0` precede the first `1` and the first `1` precede first `2`.

A

`"^(14)C_(5)xx^(8)C_(6)`

B

`"^(14)C_(5)xx^(8)C_(4)`

C

`"^(14)C_(6)xx^(8)C_(4)`

D

`"^(14)C_(6)xx^(8)C_(6)`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` Put `a` in the first positiion, (`1` way) . Pick five other positions for the remaining `0'`s )`.^(14)C_(5)`ways), put a `1` in the first of the reamining positions (`1`way), then arrange the remaining four `1'`s (`.^(8)C_(4)` ways)
`:. ^(14)C_(5)xx^(8)C_(4)`
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