Omar wants to buy a double scoop ice cream cone. His favorite flavors are vanilla, strawberry, raspberry and chocolate. A combination with both scoops of raspberry represents ___ out of ___ possible combinations.
4 C 2 = combination of 4, taken 2 at a time
C(4,2) = (4!/(4 - 2)!)/2! = 4!/(2!2!)
C(4,2) = (4x3x2x1)/(2x1x2x1)= 24/4 = 6
total of 6 combinations
1 out of 6 possible combinations
I am not a tutor
To find the number of possible combinations with both scoops of raspberry, we need to determine the total number of possible combinations of flavors on a double scoop ice cream cone.
Since Omar has four favorite flavors (vanilla, strawberry, raspberry, and chocolate), and he wants to choose two flavors for his double scoop, we can use the concept of combinations.
The formula to calculate combinations is:
nCr = n! / (r!(n-r)!)
where n represents the total number of items and r represents the number of items we want to choose.
In this case, n = 4 (the number of favorite flavors) and r = 2 (the number of scoops on the cone).
Using the formula, we can calculate the number of combinations as follows:
4C2 = 4! / (2!(4-2)!)
= 4! / (2!2!)
= (4 * 3 * 2 * 1) / ((2 * 1)(2 * 1))
= 24 / 4
= 6
So, there are a total of 6 possible combinations of flavors on the double scoop ice cream cone.
Now, to find the specific combination with both scoops of raspberry, we need to determine how many of these combinations include raspberry as one of the flavors.
From the remaining two flavors, i.e., vanilla, strawberry, and chocolate, Omar can choose one flavor to pair with the raspberry scoop.
Therefore, the combination with both scoops of raspberry represents 1 out of the 6 possible combinations.
Thus, the combination with both scoops of raspberry represents 1 out of 6 possible combinations.