How many ways can you arrange the letters in the word 'BOOK'?

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Question: How many ways can you arrange the letters in the word \'BOOK\'?

Options:

Correct Answer: 16

Solution:

The number of arrangements is 4! / 2! = 12, since \'O\' repeats.

How many ways can you arrange the letters in the word 'BOOK'?

How many ways can you arrange the letters in the word 'BOOK'?

Step 1: Count the total number of letters in the word 'BOOK'. There are 4 letters: B, O, O, K.
Step 2: Calculate the total arrangements if all letters were unique. This is done using the factorial of the number of letters, which is 4!.
Step 3: Calculate 4! (4 factorial). This means 4 x 3 x 2 x 1 = 24.
Step 4: Identify any repeating letters. In 'BOOK', the letter 'O' repeats 2 times.
Step 5: Calculate the factorial of the number of times the repeating letter occurs. For 'O', it is 2!, which is 2 x 1 = 2.
Step 6: Divide the total arrangements by the arrangements of the repeating letters. So, we do 4! / 2! = 24 / 2 = 12.
Step 7: The final answer is that there are 12 different ways to arrange the letters in the word 'BOOK'.

Permutations with Repetition – This concept involves calculating the number of distinct arrangements of letters in a word where some letters may repeat.