Question

1. An ice cream store manufactures five basic flavors (vanilla, chocolate, mint, strawberry, and fudge) of ice cream, and then creates its specialty flavors by mixing two or more basic flavors in equal proportions (a) How many specialty flavors can be obtained by mixing three basic flavors? How many of these contain chocolate? How many of these contain either chocolate or fudge or both? How many of these contain eiterhocolate or fudge but not both? (b) How many distinct flavors (including basic and specialty flavors) of ice cream can the store offer? Optional: What's the name of the store?

Answer 1

Given flavors are: (Vanilla, Chocolate, Mint, Strawberry, and Fudge). We will use combination method.

Total number of combination by mixing two or more basic flavors.

= 5c2+5c3+5c4+5c5
= 10+10+ 5+1= 26 Ans.

1. 1) No. of specialty flavors can be obtained by mixing three basic flavors:

                 5c3 = 10 ANS

2) No. of flavours containing either chocolate or fudge or both.      

= (chocolate or fudge)*(other two flavor)+(chocolate and    fudge)*(any flavor)

= 1*3c2*2 + 1*1*3c1 (here 2 is multiplied because of keyword either)

= 1*3*2 + 1*1*3

=6+3 = 9

            2) No ) No. of flavors containing either chocolate or fudge but not both

= (chocolate or fudge)*(other two flavor)

=1*3c2*2 (here 2 is multiplied because of keyword either)

=1*3*2

=6 ANS

b) Total no. of distinct flavors in the store (including basic and specialty flavors)

= 5c1+5c2+5c3+5c4+5c5

= 5+10+10+5+1= 31 ANS