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9 September, 07:11

How many committees of 4 members can be formed from 9 people?

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Answers (1)
  1. 9 September, 09:26
    0
    Answer:A

    )

    126

    different committees

    B

    )

    21

    different committees

    C

    )

    70

    different committees

    Explanation:Explanation:

    Recall: The number of different ways of arranging

    n

    numbers is

    n

    !

    If 4 people are to be selected from 9 people:

    There are 9 different choices for the first person.

    There are 8 different choices for the second person.

    There are 7 different choices for the third person.

    There are 6 different choices for the fourth person.

    This gives

    9

    *

    8

    *

    7

    *

    6

    different committees, however this will include the same combinations of people.

    There are

    4

    *

    3

    *

    2

    *

    1

    ways in which 4 people can be chosen.

    A) Therefore, for 4 people chosen from 9 there are

    9

    *

    8

    *

    7

    *

    6

    *

    5

    4

    *

    3

    *

    2

    *

    1

    =

    126

    different committees.

    B) If two people must stand, there are 2 people to be chosen from the remaining 7. Applying the same thinking as above this gives:

    7

    *

    6

    2

    =

    21

    different committees.

    C) if either one or the other must stand there are then 3 people who must be chosen from the remaining

    7

    people;

    7

    *

    6

    *

    5

    3

    *

    2

    *

    1

    =

    35

    But this can happen in 2 different ways, depending on whether John or Barbara are on the committee.

    So,

    2

    *

    35

    =

    70

    different committees can be formed.
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