Question: How many ways can 4 different letters be chosen from the word \'COMBINATION\'?
Options:
210
126
70
84
Correct Answer: 210
Solution:
The number of ways to choose 4 letters from 11 distinct letters is 11C4 = 330.
How many ways can 4 different letters be chosen from the word 'COMBINATION'?
Practice Questions
Q1
How many ways can 4 different letters be chosen from the word 'COMBINATION'?
210
126
70
84
Questions & Step-by-Step Solutions
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 7: Therefore, the number of ways to choose 4 different letters from the word 'COMBINATION' is 70.
Combinatorics – The problem tests the understanding of combinations, specifically how to choose a subset of items from a larger set without regard to the order of selection.
Distinct Elements – The question emphasizes the importance of recognizing that the letters in 'COMBINATION' are distinct for the purpose of combination calculations.
Soulshift Feedback×
On a scale of 0–10, how likely are you to recommend
The Soulshift Academy?
