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## Homework Statement

So i have this 4 problems that i already answered, but i want to know if im right.

1.- how many 4 letter words can be made with the letters of the word "emulsion" if you can use 2 vocals and 2 consonants.

My answer: 864 4*4*3*3*3!

2._ how many triangles can you make with 8 stones if you can't put more that 3 of them in a straight line

My answer: 8C3 = 56

3._ Find the term that has an x¹² in (-.333x^3+.666y^2)^8

My answer: .86x^12 y^8

4._ If i want to arrange 5 history books, 4 math books and 3 physics books in a shelve, how many ways are there to do it if i want all the books from the same topic in together?

My answer: 5!*4!*3!*3!= 103680