Problema Solution
The Cuisine Club is hosting a make your own sundae. They brought caramel, hot fudge, marshmallow, nuts, strawberries, whipped cream and pineapple. Assuming there is just vanilla ice cream, how many different different sundaes can be made by varying the combination of toppings? Be sure to include a sundae with no toppings. Describe any patterns you see in your answer.
Answer provided by our tutors
ok, ordinary sundeee is 1 possibility ot C(7,0) - seven possibilities and 0 chosen.
sundee with 1 topping is 7 possibilities. or C(7,1) - 7 possibilities and 1 chosen and so on.
with two toppings it is C(7,2)
with 3 it is C(7,3)
with 4 it is C(7,4)
up to C(7,7)
where C means combinations.
So total number of possibilities is: 1 + 7 + C(7,2) + C(7,3) + ... + C(7,7)
Assume order of toppings does not matter, i.e. nuts and pinaple is the same as pinapple nuts :)