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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?

2 Answers

6 votes
He can make 10 different styles of bracelet
User LukLed
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4 votes

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.

User Olovholm
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6.9k points