中5級的數學題?5點

Mr Chan wants to invite 6 friends from a list of 9 friends to his party,find number of ways to select guest if

1. 2 of his friends cannot be invited together

2. 2 of his friends either be invited together or not be invited together

1 Answer

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  • 10 years ago
    Favorite Answer

    1) Method 1 :All ways - 2 of his friends be invited together ways= 9C6 - (2C2) * (9-2)C(6-2)

    = 9C6 - 7C4

    = 84 - 35

    = 49 ways.

    Method 2 :None of the 2 friends be invited ways + only 1 out of the 2 friends be invited ways

    = (9-2)C6 + (2C1) (9-2)C(6-1)

    = 7C6 + 2 * 7C5

    = 7 + 2 * 21

    = 49 ways

    Method 3 :At most 1 out of the 2 friends be invited ways

    = Only 1 out of the 2 friends be invited ways - None of the 2 friends be invited ways

    = (2C1) * (9-1)C6 - (9-2)C6

    = 2 * 8C6 - 7C6

    = 2 * 28 - 7

    = 49 ways

    2)Method 1 : Be invited together ways + not be invited together ways

    = All ways

    = 9C6

    = 84 ways

    Method 2 :Be invited together ways + not be invited together ways

    = Be invited together ways + At most 1 out of the 2 friends be invited ways

    = (2C2) * (9-2)C(6-2) + (2C1) * (9-1)C6 - (9-2)C6

    = 35 + 49

    = 84 ways

    2011-05-10 16:55:20 補充:

    Corrections of Q2) :

    Method 1 :

    be invited together ways + not be invited together ways

    = (2C2) * (9-2)C(6-2) + (9-2)C6

    = 35 + 7

    = 42 ways

    2011-05-10 16:55:26 補充:

    Method 2 :

    be invited together ways + not be invited together ways

    = All ways - only 1 out of the 2 friends be invited ways

    = 9C6 - (2C1) (9-2)C(6-1)

    = 84 - 42

    = 42 ways

    2011-05-10 16:56:17 補充:

    Corrections of Q2) :

    Method 1 :

    be invited together ways + not be invited together ways

    = (2C2) * (9-2)C(6-2) + (9-2)C6

    = 35 + 7

    = 42 ways

    2011-05-10 16:56:32 補充:

    Method 2 :

    be invited together ways + not be invited together ways

    = All ways - only 1 out of the 2 friends be invited ways

    = 9C6 - (2C1) (9-2)C(6-1)

    = 84 - 42

    = 42 ways

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