Legislative Committee A legislative committee consists of 5 Democrats and 4 Republicans. A delegation of 3 is to be selected to visit a smal

Question

Legislative Committee A legislative committee consists of 5 Democrats and 4 Republicans. A delegation of 3 is to be selected to visit a small Pacific island republic. (a) How many different delegations are possible? (b) How many delegations would have all Democrats? (c) How many delegations would have 2 Democrats and 1 Republican? (d) How many delegations would include at least 1 Republican?

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Brielle 3 weeks 2022-01-01T17:05:05+00:00 1 Answer 0 views 0

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    2022-01-01T17:06:30+00:00

    Answer:

    Step-by-step explanation:

    GIVEN: Legislative Committee A legislative committee consists of 5 Democrats and 4 Republicans. A delegation of 3 is to be selected to visit a small Pacific island republic.

    TO FIND: (a) How many different delegations are possible? (b) How many delegations would have all Democrats? (c) How many delegations would have 2 Democrats and 1 Republican? (d) How many delegations would include at least 1 Republican.

    SOLUTION:

    (a)

    Total members =9

    Total delegation possible=^9C_3=\frac{9!}{6!3!}

                                             =\frac{9\times8\times7}{6}=84

    (b)

    Total democrats =5

    Total delegation possible with all democrats =^5C_3=\frac{5!}{3!2!}

                                                                              =10

    (c)

    Total democrats =4

    Total republicans =5

    Total delegations with 2 democrats and 1 republican =^4C_1\times^5C_2=\frac{4!}{3!1!}\times\frac{5!}{2!3!}

                                                                                           =4\times10=40

    (d)

    Total republicans =4

    Total delegation with at least 1 republican =\text{total delegation possible}-\text{total delegation with all democrats}

    putting values from part (a)  and (b)

    Total delegation with at least 1 republican =84-10=74

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