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 $n = \frac{N!}{(N - n)!*n!}$

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: $\frac{10!}{(10 - 6)!*6!} = \frac{10*9*8*6}{4*3*2} = 10*9*2 = 90*2 = 180$

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