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Math Help - combinations

  1. #1
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    combinations

    a delegation of 4 students is to be selected from 12 students in how many ways the delegation can be selected1. if two particular students wish to be included together only
    2.if two particular students refuse to come together and two other particular student wish to be together only in delegation
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  2. #2
    MHF Contributor Unknown008's Avatar
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    1.

    First situation:
    Put the two students together. This means there are two vacant 'slots' for 10 remaining students.

    Second situation:
    None of the two concerned students are in the delegation, which means, you have 4 vacant slots for 10 students.

    2. For this one, let A B C D E F G H I J K L be the students.

    A and B want to be together, and C and D refuse to be together in the delegation.

    Possible situations:
    (i) A and B are in the delegation with any of E to L students.
    (ii) A and B are in the delegation with C and any other student besides D.
    (iii) A and B are in the delegation with D and any other student besides C.
    (iv) Any of E through L students are in the delegation.
    (v) C and any other student from E to L are in the delegation.
    (vi) D and any other student from E to L are in the delegation.

    Can you work those out?
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