there are 7 toppings. if a sundae must have 4 toppings how many combinations can you make
There are 35 possible combinations.
This can be calculated using the combination formula:
nCr = n! / (r! * (n-r)!)
Where n is the total number of toppings (7) and r is the number of toppings needed for each sundae (4).
So, nCr = 7! / (4! * (7-4)!) = 35
what if there were only 6 toppings
If there were only 6 toppings, the number of possible combinations for a sundae with 4 toppings would be:
nCr = 6! / (4! * (6-4)!) = 15
Therefore, there would be 15 possible combinations of 4 toppings from the 6 available.
To calculate the number of combinations, we can use the concept of combinations in mathematics.
In this case, you want to find the number of combinations of 7 toppings taken 4 at a time. This can be calculated using the formula for combinations, which is:
C(n, r) = n! / (r!(n-r)!)
Where "n" represents the total number of toppings and "r" represents the number of toppings to be selected for each combination.
In your case, substituting the values into the formula gives us:
C(7, 4) = 7! / (4!(7-4)!)
Simplifying further:
C(7, 4) = (7 * 6 * 5 * 4!) / (4! * 3 * 2 * 1)
The factorials cancel out:
C(7, 4) = 7 * 6 * 5 / (3 * 2 * 1)
Simplifying the multiplication:
C(7, 4) = 7 * 5
Calculating the final answer:
C(7, 4) = 35
So, there are 35 different combinations of 4 toppings that can be made from a selection of 7 toppings.