Answer: 1) 390625, 2) 1365, 3) 411105.
Step-by-step explanation:
Since we have given that
Number of types of cupcakes = 5
Number of chocolate type = 1
1/ How many different selections of 8 cupcakes are there?
Number of cupcakes we need to select = 8
Since we have 5 options for each 8 cupcakes.
So, the number of ways to select 8 cupcakes would be :
[tex]5^8=390625[/tex]
2/ How many different selections of 8 cupcakes have at least 3 chocolate cupcakes?
Number of different selection would be :
=[tex]4^5+4^4+4^3+4^2+4+1=1365[/tex]
3/ How many different selections of 8 cupcakes have at most 2 chocolate cupcakes?
Number of ways to select no chocolate + Number of ways to select 1 chocolate + Number of ways to select 2 chocolate
[tex]5^8+4^7+4^6=411105[/tex]
Hence, 1) 390625, 2) 1365, 3) 411105.
