Permutations and Combinations question.?

Question

The chocolate factory classifies its candies as caramels (10 types), chocolate (7 types), and dark chocolate (8 types). A customer has ordered an assortment to consist of six types of caramels, four types of chocolate, and five types of dark chocolates. How many such assortments are possible?

The answer is 411,600.

I tried solving it but I don't know how to get it.

Can someone explain to me how to solve it?

Answer 1

2+2=4

Answer 2

This is the combination problem

the way to have six types of caramels from 10 types of caramels is

10!/(6!*4!)= 210

the way to have four types of chocolate from 7 types of chocolate is

7!/(4!*3!)=35

the way to have 5 types of dark chocolates from 8 types of dark chocolate is

8!/(5!*3!)=56

multiple them togeter

210*35*56=411600

Answer 3

well you do the  factorial (!)

so you have 10 types of caramel an you want to ASSORT them so you do 10 factorial or !10; but the catch is that he wants only 6 types of caramel; so instead of doing 10x9x8x7x6x5x4x3x2x1 you are only going to do 10x9x8x7x6x5 because he has 6 spaces; in this case 6 caramels so you get your answer by this formula

the same goes for chocolate he has 7 types of chocolate and he wants to assort them in 4 spaces, for the 1st slot you have 7 choices, the second you have 6 the third space you have 5 then the fourth slot you have 4, that's how you get 7x6x5x4 then you do this formula (same concept as the caramel just explained differently)

for dark chocolate it would be 8x7x6x5x4 do u understand why ?