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Math Help - Stats help (combinations/ order prb)

  1. #1
    Kradano
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    Stats help (combinations/ order prb)

    Due in 3 hours….. (1pm mt time)
    I have played with these for an hr and i have completed all homework except thiese 2 problems please help.....

    Question 1 (complete all 3 parts)
    From a group of 9 novels 7 history books and 4 self help books:

    A)In how many different ways can 4 books be chosen so that 2 of them are novels and 2 of them are history books?

    B) In how many different ways can 5 books be chosen so that there are either 0 or 1 novels ?

    C) If 5 books are chosen at random, what is the probability that at least one of each type is chosen?


    Question 2 (Completed all 4 parts)
    A line is formed from a group of 4 girls and 3 boys:

    A) How many different lines begin with a girl and end with a boy?


    B) How many different lines have the individuals alternating by gender?


    C)If all lines are equally likely, what is the probability that the line begins with a girl and ends with a boy

    D)If all lines are equally likely what is the probability that the line begins and ends with individuals of the same gender?
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  2. #2
    Super Member

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    Hello, Kradano!

    1) From a group of 9 novels, 7 history books, and 4 self-help books:

    A) In how many different ways can 4 books be chosen so that:
    2 of them are novels and 2 of them are history books?

    There are: . {9\choose2} = 36 ways to choose two Novels.
    There are: . {7\choose2} = 21 ways to choose two History books.

    Therefore, there are: . 36 \times 21 \:=\:\boxed{756\text{ ways}}



    B) In how many different ways can 5 books be chosen so that:
    there are either 0 or 1 novels ?

    To have 0 Novels, we choose 5 from the other 11 books.
    . . There are: . {11\choose5} \:=\:462 ways.

    To have 1 Novel, we choose 1 Novel from the 9 Novels and 4 from the other 11 books.
    . . There are: . {9\choose1}{11\choose4} \:=\:9\cdot330 \:=\:2970 ways.

    Therefore, there are: . 462 + 2970 \:=\:\boxed{3432\text{ ways}}




    C) If 5 books are chosen at random, what is the probability that
    at least one of each type is chosen?

    I'm still working on this part . . .

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