Answer:
The number of double dip sundae that can be created with 1 topping is:
825
Step-by-step 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.
[tex](10_C_{2}+10)\times 15[/tex]
As [tex]10_C_2[/tex] 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,
[tex](10_C_{2}+10)\times 15=(\dfrac{10!}{2!\times (10-2)!}+10)\times 15\\\\=(\dfrac{10!}{2!\times 8!}+10)\times 15\\\\\\=(45+10)\times 15\\\\\\=55\times 15\\\\\\=825[/tex])
