Final answer:
When choosing 3 letters from a set of 8, the number of possible combinations is calculated using the formula C(n, r) = n! / (r!(n-r)!), which gives us 56 possible outcomes.
Step-by-step explanation:
To calculate the number of possible outcomes when choosing 3 letters from a given set of 8 letters (A, B, C, D, E, F, G, H), you can use the combination formula. In mathematics, combinations are selections of items where the order does not matter. To find the number of combinations of n items taken r at a time, you would use the formula:
C(n, r) = n! / (r!(n-r)!)
Here, n is the total number of items to choose from, and r is the number of items to be chosen. The exclamation point (!) represents a factorial, which is the product of an integer and all the integers below it down to 1.
In this example:
- n = 8 (the total letters)
- r = 3 (the number of letters to choose)
So our calculation will be:
C(8, 3) = 8! / (3!(8-3)!) = 8! / (3!5!) = (8×7×6) / (3×2×1) = 56
Therefore, there are 56 possible outcomes when choosing 3 letters at a time from a set of 8 letters.
To find the number of possible outcomes when choosing 3 letters at a time from a set of 8 letters, we can use the concept of combinations. A combination is a selection of items in which the order does not matter. Using the formula for combinations, which is nCr = n! / ((n-r)! * r!), where n is the total number of items and r is the number of items chosen, we can calculate the number of possible outcomes.
In this case, we have 8 letters to choose from and we want to choose 3 letters at a time. So the calculation would be:
nCr = 8! / ((8-3)! * 3!)
Calculating this expression would give us the final answer.