Given : The total number of books = 4
To find : Number of ways in which these 4 books can be arranged in a shelf
Formula used :
Number of arrangements of n things taken all at a time = P(n, n)
∵ P(n, r) = \(\frac{n!}{(n-r)!}\)
∴ The total number of ways
= the number of arrangements of 4 things taken all at a time
= P(4, 4)
= \(\frac{4!}{(4-4)!}\)
= \(\frac{4!}{0!}\)
{∵ 0! = 1}
= 4 × 3 × 2 × 1
= 24
Hence,
Number of ways in which these 4 books can be arranged in a shelf are 24.