In how many ways can 3 different letters be chosen from the word 'COMPUTE'? (201

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Question: In how many ways can 3 different letters be chosen from the word \'COMPUTE\'? (2019)

Options:

Correct Answer: 70

Exam Year: 2019

Solution:

The number of ways to choose 3 letters from 8 is C(8, 3) = 56.

In how many ways can 3 different letters be chosen from the word 'COMPUTE'? (2019)

In how many ways can 3 different letters be chosen from the word 'COMPUTE'? (2019)

Step 1: Identify the total number of letters in the word 'COMPUTE'. There are 8 letters: C, O, M, P, U, T, E.
Step 2: Understand that we want to choose 3 different letters from these 8 letters.
Step 3: Use the combination formula C(n, r) to find the number of ways to choose r items from n items. Here, n is 8 (total letters) and r is 3 (letters to choose).
Step 4: The combination formula is C(n, r) = n! / (r! * (n - r)!).
Step 5: Plug in the values: C(8, 3) = 8! / (3! * (8 - 3)!) = 8! / (3! * 5!).
Step 6: Calculate 8! = 8 × 7 × 6 × 5! (the 5! cancels out).
Step 7: Now we have C(8, 3) = (8 × 7 × 6) / (3 × 2 × 1).
Step 8: Calculate the numerator: 8 × 7 × 6 = 336.
Step 9: Calculate the denominator: 3 × 2 × 1 = 6.
Step 10: Divide the numerator by the denominator: 336 / 6 = 56.
Step 11: Therefore, the number of ways to choose 3 different letters from 'COMPUTE' is 56.

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.
Counting Principles – It assesses the ability to apply counting principles to determine the number of ways to select items from a group.