Question

How many ways can 8 books be arranged on a shelf? Show all of your work for full credit.

Answer 1

Answer:

There are 40,320 ways, in which 8 books can be arranged on a shelf.

Solution:

Here, we are to find the number of ways in which 8 books can be arranged on a shelf. The total number of books is 8 and the way of arranging books is also 8.

• If one book is placed in the first place, then 7 books will be placed in front of it. If 2 books are placed in the 2nd place, then only 6 books can be placed after that book. This sequence will continue till 1 .

Permutations :

• A permutation is an arrangement of objects in a definite order.

➲ P ( n, r )= n ! / ( n - r ) !

• n = total number of objects

• r = number of objects selected

The number of ways to arrange 8 books on a shelf will be :

➝ P ( n, r ) = n ! / ( n - r ) !

➝ P ( n, r ) = 8 ! / ( 8 - 8 ) !

➝ P ( n, r ) = 8 ! / 0 !

➝ P ( n, r ) = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 / 1

➝ P ( n, r ) = 40, 320

‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ~ Hence, there are 40,320 ways in which 8 books can be arranged on a shelf !