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mote1985 [20]
2 years ago
7

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

Mathematics
1 answer:
Talja [164]2 years ago
7 0
<h3>Answer:</h3>

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

<h3>Solution:</h3>

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 .

<u>Permutations </u><u>:</u>

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

➲<u> P ( n, r )= n ! / ( n - r ) !</u>

  • 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 <u>40,320 ways</u> in which 8 books can be arranged on a shelf !

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