) In how many ways can 5 different novels, 2 different mathematics books, and 1 biology book be arranged on a bookshelf if (a) the books can

Question

) In how many ways can 5 different novels, 2 different mathematics books, and 1 biology book be arranged on a bookshelf if (a) the books can be arranged in any order? Answer: 40320 (b) the mathematics books must be together and the novels must be together? Answer: (c) the mathematics books must be together but the other books can be arranged in any order? Answer:

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Eloise 2 weeks 2021-11-22T02:16:58+00:00 1 Answer 0

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    2021-11-22T02:18:40+00:00

    Answer:

    a. 40320

    b. 1440

    c. 10080

    Step-by-step explanation:

    Number of Novels: 5

    Numbers of Mathematics books: 2

    Number of biology: 1

    a. If the books are to be arranged in any order

    Total number of books = 5 + 2 + 1 = 8

    Number of Arrangements = 8!

    Number of Arrangements = 8*7*6*5*4*3*2*1

    Number of Arrangements = 40320 ways

    b. The mathematics books must be together and the novels must be together

    To get the number of possible arrangements

    First, Calculate the Possible Arrangements of Mathematics Books;

    Number of Mathematics Books = 2

    Arrangements = 2!

    Arrangements = 2*1 = 2

    Then, Calculate the Possible Arrangements of Novel Books;

    Number of Novel Books = 5

    Arrangements = 5!

    Arrangements = 5*4*3*2*1

    Arrangements = 120

    Then Calculate the Possible Arrangements of the Mathematics book bundle, Novel Bundle with Biology book.

    The mathematics book bundled together is 1

    The novel bundled together is 1

    Other books = 1 Biology

    Total = 3

    Arrangements = 3!

    Arrangements = 3*2*1 = 6

    Total Arrangements = 2 * 120 * 6

    Total Arrangements = 1440

    c. If the mathematics book must be together but other books can be arranged in any order

    To get the Number of Possible Arrangements

    First, Calculate the Possible Arrangements of Mathematics Books;

    Number of Mathematics Books = 2

    Arrangements = 2!

    Arrangements = 2*1 = 2

    Then Calculate the Possible Arrangements of the Mathematics book bundle with other books;

    The mathematics book bundled together is 1

    Other books = 5 Novels + 1 Biology

    Total = 7

    Arrangements = 7!

    Arrangements = 7*6*5*4*3*2*1

    Arrangements = 5040

    Total Possible Arrangements = 2 * 5040 = 10080 ways

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