The following formula is used to calculate the number of possible combinations of letters:
\[ C = \frac{n!}{r!(n-r)!} \]
Where:
A letter combination refers to the arrangement of letters in a specific order. It can be a part of a word, a whole word, or a series of words. These combinations can be used in various fields such as cryptography, linguistics, and computer science. In the English language, certain combinations are more common than others, and understanding these can help in areas such as spelling, pronunciation, and language learning.
Let's assume the total number of letters (n) is 5, and we want to choose 3 letters at a time (r):
Step 1: Calculate the factorial of the total number of letters:
\[ 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 \]
Step 2: Calculate the factorial of the number of letters to be chosen at a time:
\[ 3! = 3 \times 2 \times 1 = 6 \]
Step 3: Calculate the factorial of the difference between the total number of letters and the number of letters to be chosen at a time:
\[ (5 - 3)! = 2! = 2 \times 1 = 2 \]
Step 4: Apply the formula:
\[ C = \frac{120}{6 \times 2} = \frac{120}{12} = 10 \]
So, the number of possible combinations is 10.