Three of 16 toppings can be selected for dressing up a cup of frozen yogurt. How many ways of a cup frozen yogurt can be dressed up?
Select one:
a. 3360
b. 560
c. 48
d. 45
16C3 = 16*15*14 / 1*2*3 = 560
Well, if we have 16 toppings to choose from and we can only select 3, we can use a little math to figure out the number of ways.
We can use the combination formula, which is nCr = n! / (r!(n-r)!), where n is the total number of items and r is the number of items we want to select.
In this case, n would be 16 (the number of toppings) and r would be 3 (the number of toppings we want to select).
Plugging those numbers into the formula, we get:
16C3 = 16! / (3!(16-3)!) = 16! / (3!13!) = (16 x 15 x 14) / (3 x 2 x 1) = 3360 / 6 = 560.
So, the answer is 560, option b.
To determine the number of ways to dress up a cup of frozen yogurt with three toppings out of 16 options, we can use the combination formula.
The formula for combination is given by:
C(n,r) = n! / (r!(n-r)!)
In this case, we have 16 toppings to select from and we want to choose 3 toppings.
Using the combination formula, we can calculate the number of ways as:
C(16,3) = 16! / (3!(16-3)!)
= 16! / (3!13!)
= (16 * 15 * 14) / (3 * 2 * 1)
= 3360 / 6
= 560
Therefore, the number of ways to dress up a cup of frozen yogurt is 560.
Therefore, the correct answer is: b. 560.
To find the number of ways a cup of frozen yogurt can be dressed up with three toppings out of a total of 16, we can use the concept of combinations.
The formula for calculating the number of combinations is given by:
C(n, r) = n! / ((n - r)! * r!)
Where n is the total number of items available (16 in this case) and r is the number of items we want to choose (3 in this case).
Using the formula, we can calculate the number of combinations as follows:
C(16, 3) = 16! / ((16 - 3)! * 3!)
Calculating this expression:
C(16, 3) = 16! / (13! * 3!) = (16 * 15 * 14) / (3 * 2 * 1) = 560
Therefore, there are 560 ways a cup of frozen yogurt can be dressed up with three toppings.
So, the correct answer is b. 560.