An ice cream shop offers 7 toppings. How many 4-topping ice cream sundaes can you make?
A)11
B)28
C)30 <-- My answer
D)35
combinations of 7 taken 4 at a time
C(7,4) = 7! /[ 4!(3!)]
= 7*6*5/(3*2) = 35
To determine the number of 4-topping ice cream sundaes that can be made, you can use the concept of combinations.
In this case, we have 7 toppings to choose from, and we want to choose 4 toppings for each sundae. The formula for calculating combinations is:
nCr = n! / (r!(n-r)!)
where n is the total number of items and r is the number of items to be chosen.
Applying this formula to our situation, we have:
7C4 = 7! / (4!(7-4)!)
Simplifying further:
7C4 = (7! / (4! * 3!)
The exclamation mark represents the factorial of a number, which means multiplying a number by all positive integers less than itself. For example, 4! means 4 * 3 * 2 * 1.
Calculating the factorials:
7! = 7 * 6 * 5 * 4 * 3 * 2 * 1
4! = 4 * 3 * 2 * 1
3! = 3 * 2 * 1
Substituting the values into the combination formula:
7C4 = (7 * 6 * 5 * 4 * 3 * 2 * 1) / ((4 * 3 * 2 * 1) * (3 * 2 * 1))
Simplifying further:
7C4 = (7 * 6 * 5) / (4 * 3 * 2 * 1)
7C4 = 210 / 24
7C4 = 8.75
Since we can't have a fraction of a sundae, we need to round this number to the nearest whole number.
The correct answer is 9 sundaes, which is not among the options provided. Therefore, none of the given options (A, B, C, D) is the correct answer for how many 4-topping ice cream sundaes can be made.