In how many ways can 5 books be arranged on a shelf If 2 of the books are identical?
What is 5!/2!
To find the number of ways to arrange 5 books on a shelf where 2 of the books are identical, we can use the concept of permutations.
Step 1: Determine the total number of arrangements without considering the identical books. In this case, we have 5 books, but we should treat the identical books as one entity. So, the number of arrangements without considering the identical books is 4!.
Step 2: Account for the arrangements within the identical books. Since the identical books are indistinguishable, we need to divide the total number of arrangements from step 1 by the number of ways the identical books can be arranged. In this case, there are 2 identical books, so the number of ways they can be arranged is 2!.
Step 3: Calculate the final number of arrangements by dividing the result of step 1 by the result of step 2.
Number of arrangements = 4! / 2!
Now, let's compute it.
4! = 4 x 3 x 2 x 1 = 24
2! = 2 x 1 = 2
Number of arrangements = 24 / 2 = 12
Hence, there are 12 ways to arrange the 5 books on a shelf when 2 of the books are identical.