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 [tex]n = \frac{N!}{(N - n)!*n!}[/tex]
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: [tex]\frac{10!}{(10 - 6)!*6!} = \frac{10*9*8*6}{4*3*2} = 10*9*2 = 90*2 = 180[/tex]
So there are 180 different bracelets that the jeweler can create.
