Question

There are five identical blue books, two identical green books, and three identical black books. How many different patterns can the books be arranged on a shelf?

Answer 1

Answer:

2520 patterns

Step-by-step explanation:

In 'n' 10!  ways, books can be arranged. But, there are also 5! permutation of blue books 'n1', 2! permutation of identical green books 'n2', and 3! permutation identical black books 'n3'.

Therefore, for non identical arrangements:

$\frac{n!}{n1!n2!n3!}$

$\frac{10!}{5!2!3!}$ = 2520

Therefore, the books can be arranged on a shelf in 2520 patterns