Question

A music store has a display of 8 instruments, where 3 identical keyboards, 2 identical guitars, and 3 identical violins are shown. How many different ways can they be displayed?

Answer 1

Answer:

This is a permutations problem where we have repeats. I'm assuming that the items need to be displayed in a line, and that any two identical items can be swapped without giving a new display. There being 7 = 3 + 2 + 2 total items, there would be 7! = 7*6*5*4*3*2*1 ways of arranging them, but because of the identical items we count too many displays if we don't consider this. To account for the identical items, we divide the answer 7! by 3!, 2!, and 2! to account for each group of identical items and the number of ways we could rearrange them in their groups. So the total number of displays is 7!/(3!*2!*2!) = 210. Hope that helps!

Step-by-step explanation: