If I have 22 toppings available for a burger, how many combinations are possible
Combination Calculator. In finite mathematics a combination is most typically calculated using the formula C(n,r) = n!/r!(n-r)!. In this formula n represents the total number of items and r represents the number of items to choose. The formula is modified depending on the importance of item order and repeating items in the set of allowed results.
You won't use 22 toppings on any burger. How many toppings will you use on any one burger (r)?
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5! = 5 * 4 * 3 * 2 * 1
To find the number of combinations possible with 22 toppings for a burger, you can use the formula for combinations:
C(n, r) = n! / (r!(n-r)!)
where n is the total number of toppings available and r is the number of toppings you want to choose for each combination.
In this case, you want to choose all the toppings available (r = 22) out of 22, so the formula would be:
C(22, 22) = 22! / (22!(22-22)!)
However, since you're choosing all the toppings available, this simplifies to:
C(22, 22) = 1
Therefore, there is only 1 combination possible when you have 22 toppings available for a burger.
To calculate the number of combinations possible with 22 toppings for a burger, you can utilize the concept of combinations.
The formula to calculate combinations is:
C(n, r) = n! / (r! * (n - r)!)
Where:
C(n, r) represents the number of combinations,
n represents the total number of items available,
r represents the number of items to be selected.
In this case, you want to find the number of combinations possible with 22 toppings, assuming you can select all 22 toppings at once. Therefore, n = 22 and r = 22.
Now, let's substitute these values into the formula:
C(22, 22) = 22! / (22! * (22 - 22)!)
First, let's simplify the denominator:
(22 - 22)! = 0! = 1 (any factorial of 0 is considered 1)
Now, the equation becomes:
C(22, 22) = 22! / (22! * 1)
Next, simplify further:
22! / 22! = 1 (any factorial divided by itself is considered 1)
So, the number of combinations possible with 22 toppings is 1.