How many ways can 4 different letters be selected from the word 'COMBINATION'?

How many ways can 4 different letters be selected from the word 'COMBINATION'?

Correct Answer: 330

Step 1: Identify the total number of distinct letters in the word 'COMBINATION'.
Step 2: Count the distinct letters: C, O, M, B, I, N, A, T. There are 8 distinct letters.
Step 3: We need to select 4 letters from these 8 distinct letters.
Step 4: Use the combination formula to find the number of ways to choose 4 letters from 8. The formula is nCr = n! / (r!(n-r)!), where n is the total number of items, and r is the number of items to choose.
Step 5: Plug in the values: n = 8 and r = 4. So, we calculate 8C4.
Step 6: Calculate 8C4 = 8! / (4!(8-4)!) = 8! / (4! * 4!) = (8*7*6*5) / (4*3*2*1) = 70.
Step 7: Therefore, there are 70 ways to select 4 different letters from the word 'COMBINATION'.

Combinatorics – The question tests the understanding of combinations, specifically how to select a subset of items from a larger set without regard to the order of selection.
Distinct Elements – It emphasizes the importance of recognizing that the letters in 'COMBINATION' are distinct for the purpose of selection.