Question

A jeweler has 10 different gems he uses to create bracelets. If his bracelets have 6 different gems apiece, how many different styles of bracelets can he create?

Answer 1

He can make 10 different styles of bracelet

Answer 2

Answer: Hello there!

We know that the jeweler has 10 different gems, and we know that each bracelet has 6 different gems. We want to know the total amount of different styles of bracelets he can make:

This is obtained with the combinatory number between 10 and 6:

this is
`n = (N!)/((N - n)!*n!)`

This number says the number of combinations that we can make if we divide N objects into groups of n.

then for 10 and 6; we have:
`(10!)/((10 - 6)!*6!) = (10*9*8*6)/(4*3*2) = 10*9*2 = 90*2 = 180`

So there are 180 different bracelets that the jeweler can create.