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Let N = the number of ways of choosing 1...

Let N = the number of ways of choosing 10 objects out of 31 objects of which 10 are identtical and the remaining are distinct, then `2^(-22)` N = ________

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Statement 1: Number of ways of selecting 10 objects from 42 objects of which 21 objects are identical and remaining objects are distinct is 2^(20). Statement 2: 42.Statement 2: 42C_(0)+^(42)C_(1)+^(42)C_(2)+...+^(42)C_(21)=2^(41)

Prove that the number of ways to select n objects from 3n objects of whilch n are identical and the rest are different is 2^(2n-1)+((2n)!)/(2(n!)^(2))

Knowledge Check

  • The number of ways of choosing 10 objects out of 31 objects of which 10 are identical and the remaining 21 are distinct, is

    A
    `2^(20) - 1`
    B
    `2^(21)`
    C
    `2^(20)`
    D
    `2^(20) + 1`

  • The number of ways of choosing 10 objects out of 31 of which 10 are identical and the remaning 21 are distinct, is

    A
    `2^(20)-1`
    B
    `2^(20)`
    C
    `2^(21)`
    D
    `2^(20)+1`

  • The number of ways of choosing n objects out of (3n+1) objects of which n are identical and (2n+1) are distinct, is

    A
    `2^(2n)`
    B
    `2^(2n+1)`
    C
    `2^(2n-1)`
    D
    none of these

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    Find the number of ways of selecting 3 pairs from 8 distinct objects.

    The number of ways in which n distinct objects can be put into two identical boxes so that no box remains empty, is

    The number of selection of n objects from 2n objects of which n are identical and the rest are different is

    Which of the following is noth the number of ways of selecting n objects from 2n objects of which n objects are identical

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