How many ways can 4 different letters be chosen from the word 'COMPUTE'? (2022)

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Question: How many ways can 4 different letters be chosen from the word \'COMPUTE\'? (2022)

Options:

Correct Answer: 56

Exam Year: 2022

Solution:

The number of ways is 8C4 = 70.

How many ways can 4 different letters be chosen from the word 'COMPUTE'? (2022)

How many ways can 4 different letters be chosen from the word 'COMPUTE'? (2022)

Step 1: Identify the total number of different letters in the word 'COMPUTE'. There are 8 letters: C, O, M, P, U, T, E.
Step 2: Determine how many letters you want to choose. In this case, we want to choose 4 letters.
Step 3: Use the combination formula to find the number of ways to choose 4 letters from 8 letters. 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 4: Plug in the values into the formula: 8C4 = 8! / (4! * (8 - 4)!) = 8! / (4! * 4!).
Step 5: Calculate the factorials: 8! = 40320, 4! = 24. So, 8C4 = 40320 / (24 * 24) = 40320 / 576.
Step 6: Perform the division: 40320 / 576 = 70.
Step 7: Conclude that there are 70 different ways to choose 4 letters from the word 'COMPUTE'.

Combinatorics – The question tests the understanding of combinations, specifically how to choose a subset of items from a larger set without regard to the order of selection.
Counting Principles – It also assesses the ability to apply counting principles to determine the number of ways to select items from a set.