An ice cream shop offers the toppings shown below. How many 4-topping ice cream sundaes can you make?
chocolate chips
walnuts
strawberry sprinkles
caramel
hot fudge
whipped cream
gummy bears
11
28 **
30
35
7C4 = 7*6*5*4/4! = 35
There are 28 2-topping sundaes
7!/4!3!
7* 6* 5 * 4* 3 *2 *1 divided by
4*3* 2* 1* 3*2*1
You can cancel like factors
7(6)5) divided by (3)2 = 35
thank you
thank you
To find the number of 4-topping ice cream sundaes that can be made, we need to use combinations.
Combinations represent the different ways we can select a certain number of items from a larger group, without considering the order in which they are selected.
In this case, we have 7 toppings to choose from and we want to select 4 toppings for each sundae.
The formula to calculate combinations is given by:
C(n, r) = n! / (r!(n-r)!)
Where:
- n represents the total number of items (toppings in this case),
- r represents the number of items to be selected (4 toppings),
- "!" denotes the factorial operation.
Plugging in the values:
C(7, 4) = 7! / (4!(7-4)!)
= 7! / (4!3!)
Using the factorial definition:
7! = 7 * 6 * 5 * 4!
4! = 4 * 3 * 2 * 1
3! = 3 * 2 * 1
We can simplify the expression:
C(7, 4) = (7 * 6 * 5 * 4!) / (4 * 3 * 2 * 1 * 3 * 2 * 1)
= (7 * 6 * 5) / (3 * 2 * 1)
= (7 * 6 * 5) / (3 * 2)
= 35
Therefore, the number of 4-topping ice cream sundaes that can be made is 35.