Question

ALlice, Bob, and Kevin go to an ice cream shop that sells 7 different flavors of ice cream:chocolate, vanilla, mint chip, strawberry, cookie dough, banana, and caramel. They decide to eachorder 9 scoops of ice cream. The order in which they order the scoops does not matter (all thatmatters is how many of each flavor that they order).(a) Alice sees all the flavors and they all look so good that she decides she wants to try asmany as possible. How many ways can she choose her 9 scoops so she gets at least 1 scoop ofeach flavor? What word describes the type of function from Alice's 9 scoops to the 7 flavors?(b) Bob's stomach hurts if he eats too much mint. How many ways can Bob choose his 9scoops so that he gets no more than 4 scoops of mint chip?C is Kevin sees all the flavors and decides he wants to try the fruit flavors. How many ways can she order at least 3 schools of strawberry or atleast 3 schools of banana

Answer 1

Alice has 36 possibilities of choosing ,Bob 126 and Kevin 84.

Alice, Bob and Kevin

7 different Flavors:

Chocolate

Vanillla

mint chip

strawberry

cookie dough

banana

caramel

The order of the 9 scoops does not matter.

_ _ _ _

a) How many ways can she choose her 9 scoops so she gets at least 1 scoop of each flavor?

Since there are 7 flavors, and she wants at least one of each then we have:

$C=\frac{9!}{7!2!}\text{ =3}6$

Alice has 36 possibilites of choosing

b) Bob

Since Bob can't eat too much he can't do no more than 4

$C\text{ =}\frac{9!}{4!5!}=126$

Bob has 126 possibilities of making his choice.

c) Kevin

3 scoups of banana or 3 scoups of strawberries.

Considering He wants 9 scoups.

$C=\frac{9!}{6!3!}=84$

Kevin has 84 possibilities for banana or strawberries