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The set S""=""{1,""2,""3,"" ,""12) is...

The set `S""=""{1,""2,""3,"" ,""12)` is to be partitioned into three sets A, B, C of equal size. Thus, `AuuBuuC""=""S ,""AnnB""=""BnnC""=""AnnC""=varphi` . The number of ways to partition S is (1) `(12 !)/(3!(4!)^3)` (2) `(12 !)/(3!(3!)^4)` (3) `(12 !)/((4!)^3)` (4) `(12 !)/((4!)^4)`

Text Solution

Verified by Experts

`AuuBuuC=S`
`AnnB=Bnnc=AnnC=phi`
`A=^12c_4`
`B=^8c_4`
`C=^4c_4`
`AxxBxxC=^12c_4xx^8c_4xx^4c_4`
`=12!/(4!8!)xx8!/4!4!xx4!/4!`
`=12!/(4!)^3`
...
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Knowledge Check

  • The set S={1,2,3,…12} is to be partitioned into three sets A, B, C of equal size. Thus A uu B uu C=S,A nn B =B nn C=C nn A=phi . The number of ways to partition S is

    A
    `(12!)/(3!(4!)^(3))`
    B
    `(12!)/(3!(3!)^(3))`
    C
    `(12!)/((4!)^(3))`
    D
    `(12!)/((3!)^(4))`

  • The set S={1,2,3…12} is to be partitioned into three sets A, B, C of equal size such that, A uu B uu C=S,A nn B=B nn C=C nn A=phi . The number of ways to partition S is.

    A
    `(12!)/(3!(4!)^(3))`
    B
    `(12!)/(3!(3!)^(3))`
    C
    `(12!)/((4!)^(3))`
    D
    `(12!)/((3!)^(4))`

  • The set S:{1,2,3…………12} is to be partitioned into three sets A,B,C of equal size. Thus A cup B cup C=S, A cap B =B cap C=A cap C=phi The number of ways to partition S is :

    A
    `(12 !)/(3!(4!)^3)`
    B
    `(12!)/(3!(4!)^4)`
    C
    `(12!)/(3!(4!)^3)`
    D
    `(12!)/(3!)^4`