How many ways can 5 different letters be arranged if 2 letters are identical? (2

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Question: How many ways can 5 different letters be arranged if 2 letters are identical? (2017)

Options:

Correct Answer: 120

Exam Year: 2017

Solution:

The number of arrangements of 5 letters where 2 are identical is 5! / 2! = 60.

How many ways can 5 different letters be arranged if 2 letters are identical? (2017)

How many ways can 5 different letters be arranged if 2 letters are identical? (2017)

Step 1: Understand that we have 5 letters in total.
Step 2: Identify that 2 of these letters are identical.
Step 3: If all 5 letters were different, the number of arrangements would be calculated using 5! (5 factorial).
Step 4: Calculate 5! which is 5 x 4 x 3 x 2 x 1 = 120.
Step 5: Since 2 letters are identical, we need to divide by the number of arrangements of these 2 identical letters, which is 2! (2 factorial).
Step 6: Calculate 2! which is 2 x 1 = 2.
Step 7: Now, divide the total arrangements by the arrangements of the identical letters: 120 / 2 = 60.
Step 8: Therefore, the total number of ways to arrange the 5 letters with 2 identical letters is 60.

Permutations with Identical Items – This concept involves calculating the number of distinct arrangements of items where some items are identical, using the formula n! / k! where n is the total number of items and k is the number of identical items.