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

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

Correct Answer: 330

Step 1: Identify the letters in the word 'COMBINATION'. The letters are C, O, M, B, I, N, A, T, I, O, N.
Step 2: Count the unique letters. The unique letters are C, O, M, B, I, N, A, T. There are 8 unique letters.
Step 3: Understand that we want to choose 4 letters from these 8 unique 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 to choose from, and r is the number of items to choose.
Step 5: Plug in the values: n = 8 and r = 4. So, we calculate 8C4 = 8! / (4!(8-4)!) = 8! / (4! * 4!).
Step 6: Calculate 8! = 40320 and 4! = 24. So, 8C4 = 40320 / (24 * 24) = 40320 / 576 = 70.
Step 7: Therefore, the number of ways to choose 4 different letters from the word 'COMBINATION' is 70.

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