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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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Knowledge Check

  • 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)`

  • Number of all permutations of the set of four letters E , O , S , P taken two at a time is

    A
    `""^(4)C_(2)xx 2!`
    B
    `""^(4)C_(2)`
    C
    `2!`
    D
    `4!`

  • Let S be the set of all real numbers. Then the relation R= {(a,b):1+abgt0} on S is

    A
    Reflexive and symmetric but not transitive
    B
    Reflexive, transitive but not symmetric
    C
    Symmetric, Transitive but not reflexive
    D
    Reflexive, transitive and symmetric

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