How many three-letter combinations are possible using the letters D, E, F, G, and H?
6C3
combination implies that order is not a factor
WTH
To calculate the number of three-letter combinations possible using the letters D, E, F, G, and H, we need to use the concept of permutations.
A permutation is the arrangement of elements in a specific order. In this case, we want to find the number of three-letter combinations, which means the order matters.
To solve this problem, we can use the formula for permutations without repetition. The formula is:
P(n, r) = n! / (n - r)!
Where:
- n is the total number of available letters (5 in this case: D, E, F, G, H)
- r is the number of items we want to select (3 in this case, as we want to find three-letter combinations)
- ! means factorial, which is the product of a number and all the positive integers below it
Now let's substitute the values into the formula:
P(5, 3) = 5! / (5 - 3)!
Calculating the factorial values:
5! = 5 x 4 x 3 x 2 x 1 = 120
(5 - 3)! = 2! = 2 x 1 = 2
Now we can substitute the factorial values into the formula:
P(5, 3) = 120 / 2 = 60
Therefore, there are 60 possible three-letter combinations using the letters D, E, F, G, and H.