Question

Can someone explain to me how to do this? Im completely confused. Please and thanks

Answer 1

3 sundaes

Explanation:

nCk or C(n, k) is a representation of the "combinations" function. It tells you how many combinations of n things there are when they are taken k at a time.

Here, you have 3 toppings, and you want to count the number of ways you can take 2 at a time. You are being asked to find the value of 3C2, or C(3,2). You do this by putting 3 where n is in the formula, and 2 where k is. Then do the arithmetic.

The exclamation point is the factorial symbol, and it means the product of all positive integers less than or equal to the number in front of the exclamation point.* When evaluating this formula, it is often convenient to cancel like factors from numerator and denominator, so you're not trying to multiply huge numbers.

`_3C_2=(3!)/(2!(3-2)!)=(3\cdot 2\cdot 1)/(2\cdot 1\cdot(1))=3`

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The 3 different sundaes you can create are ...

(chocolate, caramel), (chocolate, strawberry), (caramel, strawberry)

When we use this formula, we're not concerned with the order of the toppings. That is, we consider a (chocolate, caramel) sundae to be exactly the same thing as a (caramel, chocolate) sundae.

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* You also need to know that 0! is defined as 1. The factorial function is only defined for non-negative integers.