Question

An art gallery has 12 vases. How many ways can 5 of the vases be arranged in the display window?

Answer 1

12 x 5 = 60 different ways

Answer 2

The number of ways of arranging 5 vases in the display window is:

95040 ways

Explanation:

We know that if we have a total of n items and we need ti arrange "r" items out of a total of n items then we need to use the method of permutation.

The formula of arranging r items out of n items is given by:

`n_P_r=(n!)/((n-r)!)`

Here in the question we have:

n=12 and r=5

Hence, the number of ways of arranging them is given by:

`{12}_P_5=(12!)/((12-5)!)\\\\\\{12}_P_5=(12!)/(7!)\\\\\\{12}_P_5=(12* 11* 10* 9* 8* 7!)/(7!)\\\\\\{12}_P_5=12* 11* 10* 9* 8\\\\\\{12}_P_5=95040`

Hence, the answer is:

95040 ways