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When you have a math problem, and it says like "You have 4 types of hats, 5 different decorations, how many combinations can you make of hat and decoration?" How would you figure it out?
Also, if the problem said "there are 4 types of hats, 5 types of decorations, and he wants one hat with 3 decorations on it. how many possibilities?"
how would you do that?
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C(4,1) x C(5,1)
4!/3!x1! (the exclamation point means factorial)
so its 4x3x2x1/3x2x1x1, you can cancel out the 3, 2, and 1 and you just get 4
5!/4!x1! 5x4x3x2x1/4x3x2x1x1, and you can cancel out the 4, 3, 2, and 1 and just get 5
multiply 5x4 and the answer to the first one is 20
and the second one is just C(4,1) x C(5,3)
C(4,1) is 4, as we already figure out
C(5,3) is 5!/3!2! which is 5x4x3x2x1/3x2x1x2x1, you can cancel out the 3, 2, and 1 and you get 5x4/2 which is 10
and 4x10 is 40 so that's the answer to the 2nd one
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