Need Some Math Help.?

The chocolate factory classifies its candies as caramels (5 types), chocolate (7 types), and dark chocolate (10 types). A customer has ordered an assortment to consist of 4 types of caramels, 5 types of chocolate, and 7 types of dark chocolates. How many such assortments are possible?


Can I assume duplicates are allowed in the assortment? For example, if there are four types of caramels in the assortment, can any of them be the same types? The problem is a lot easier if duplicates are allowed.

There are 5 types of caramel, and thus there are 5^4 possible combinations of four.

Likewise, there are 7 types of chocolate, and thus 7^5 possible combinations of five.

And 10 types of dk choc, and thus 10^7 possible combinations of seven.

The total number of possible combinations in the assortment, then, is


which is a whole bunch.


A five member committee is to be selected from among four Math teachers and five English teachers. In how many different ways can the committee be formed under the following circumstance? A) Anyone is eligible to serve on the committee. B) The committee must consist of 3 Math teachers and 2 English teachers. C) The committee must contain at least three Math teachers. D) The committee must contain at least three English teachers.