How many ways can 3 letters be chosen from the word 'COMBINATION'?

How many ways can 3 letters be chosen from the word 'COMBINATION'?

Step 1: Identify the total number of distinct letters in the word 'COMBINATION'.
Step 2: Count the letters: C, O, M, B, I, N, A, T. There are 8 distinct letters.
Step 3: Understand that we want to choose 3 letters from these 8 distinct letters.
Step 4: Use the combination formula, which is written as nCr, where n is the total number of items to choose from and r is the number of items to choose.
Step 5: In this case, n = 8 (the distinct letters) and r = 3 (the letters we want to choose).
Step 6: Calculate the combination using the formula: 8C3 = 8! / (3! * (8-3)!).
Step 7: Simplify the calculation: 8C3 = 8! / (3! * 5!) = (8 * 7 * 6) / (3 * 2 * 1) = 56.
Step 8: Therefore, there are 56 ways to choose 3 letters from the word 'COMBINATION'.

Combinatorics – The study of counting, arrangements, and combinations of objects.
Distinct vs. Non-distinct Letters – Understanding the difference between choosing from distinct letters and accounting for repeated letters.