How many ways can arrange 3 french books , 2 history books and 5maths books if all books are different

History

ScanSolve AI Answer

Answer

3,628,800

Step-by-step solution

3 steps

  1. Determine the total number of books.

    You have 3 French books, 2 History books, and 5 Math books.
    Total number of books = 3+2+5=103 + 2 + 5 = 10 books.

  2. Calculate the number of arrangements.

    Since all books are different, arranging them is a permutation of nn distinct items. The number of ways to arrange nn distinct items is n!n!.
    In this case, n=10n=10.
    So, the number of ways to arrange the 10 different books is 10!10!.

  3. Calculate the factorial.

    10!=10×9×8×7×6×5×4×3×2×110! = 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 10!=3,628,80010! = 3,628,800

    The number of ways to arrange the books is:

    3,628,8003,628,800
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