Question

A yogurt shop allows its customers to add, for no charge, 3 toppings to any yogurt purchased. If the store has 15 possible toppings, how many different 3-topping combinations can a customers choose?

Answer 1

Answer:

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Step-by-step explanation:

Answer 2

Answer:

The number of different 3-topping combinations a customers can choose is:

                                 455

Step-by-step explanation:

We know that the number of ways to choose r items out of a given n items is calculated with the help of method of COMBINATION.

The formula is given by:

              $n_C_r=\dfrac{n!}{r!\times (n-r)!}$

We have n=15 and r=3

Hence, the number of combinations possible is given by:

         ${15}_C_3=\dfrac{15!}{3!\times (15-3)!}\\\\\\{15}_C_3=\dfrac{15!}{3!\times 12!}\\\\\\{15}_C_3=\dfrac{15\times 14\times 13\times 12!}{3!\times 12!}\\\\\\{15}_C_3=\dfrac{15\times 14\times 13}{3\times 2}\\\\\\{15}_C_3=455$

                       The answer is:

                                 455