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Suppose you go to an ice cream shop which allows you to choose from 7 flavors of ice cream and 5 toppings. if you decide to get a sundae with 2 different types of ice cream and 3 different toppings, how many ways are there to make this choice?

Respuesta :

konrad509

The order doesn't matter.

[tex]k [/tex] objects can be chosen out of [tex] n [/tex] objects, when the order doesn't matter, in [tex] C(n,k)=\dfrac{n!}{k!(n-k)!} [/tex] ways.

So, the answer is [tex] C(7,2)\cdot C(5,3)=\dfrac{7!}{2!5!}\cdot\dfrac{5!}{3!2!}=\dfrac{6\cdot7}{2}\cdot\dfrac{4\cdot5}{2}=210 [/tex] ways.

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