Question

A frozen yogurt shop offers 10 different flavors of yogurt and 15 different toppings. How

many double­dip sundae combinations can be created with 1 topping? One yogurt
flavor may be used for both dips.

Answer 1

u can use 10 sundaes and 10 toppings

Answer 2

The number of double dip sundae that can be created with 1 topping is:

825

Explanation:

Since, there are 10 different flavors and same flavor can be used for both the dips.

Also, there are a total of 15 different toppings.

Hence, the number of different double dip sundae that can be created with 1 topping is:

825

( Since, the order in which the two sundae are placed does not matter. Hence, we need to use the method of combination.

`(10_C_(2)+10)* 15`

As
`10_C_2` denotes the number of ways of choosing of 2 different toppings from the 10 flavors and the addition 10 term represent the 10 cases case in which both the dips are of same flavor

Hence,

`(10_C_(2)+10)* 15=((10!)/(2!* (10-2)!)+10)* 15\\\\=((10!)/(2!* 8!)+10)* 15\\\\\\=(45+10)* 15\\\\\\=55* 15\\\\\\=825`)