How many ways can 5 different letters be arranged if 2 letters must always be together?

1 question

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Q: How many ways can 5 different letters be arranged if 2 letters must always be together?

Solution: Treat the 2 letters as one unit. So, we have 4 units to arrange: 4! * 2! = 48.

Steps: 6

Step 1: Identify the 5 different letters. Let's call them A, B, C, D, and E.
Step 2: Choose the 2 letters that must always be together. For example, let's say we choose A and B.
Step 3: Treat the 2 letters (A and B) as one single unit or block. Now, instead of 5 letters, we have 4 units to arrange: (AB), C, D, and E.
Step 4: Calculate the number of ways to arrange these 4 units. The formula for arranging n units is n!. Here, n = 4, so we calculate 4! (which is 4 x 3 x 2 x 1 = 24).
Step 5: Since A and B can be arranged within their block in 2 different ways (AB or BA), we need to multiply the arrangements of the 4 units by the arrangements of A and B. This gives us 4! * 2! = 24 * 2 = 48.
Step 6: Therefore, the total number of ways to arrange the 5 letters with A and B always together is 48.