In how many ways can the letters of the word 'BOOK' be arranged? (2022)

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Question: In how many ways can the letters of the word \'BOOK\' be arranged? (2022)

Options:

Correct Answer: 16

Exam Year: 2022

Solution:

The word \'BOOK\' has 4 letters with \'O\' repeating. The number of arrangements is 4! / 2! = 12.

In how many ways can the letters of the word 'BOOK' be arranged? (2022)

In how many ways can the letters of the word 'BOOK' be arranged? (2022)

Step 1: Identify the letters in the word 'BOOK'. The letters are B, O, O, and K.
Step 2: Count the total number of letters. There are 4 letters in total.
Step 3: Notice that the letter 'O' repeats. It appears 2 times.
Step 4: Use the formula for arrangements of letters where some letters are repeated. The formula is: Total arrangements = Total letters! / (Repeated letters!)
Step 5: Calculate the total arrangements. Here, it is 4! (for 4 letters) divided by 2! (for the 2 O's).
Step 6: Calculate 4! which is 4 x 3 x 2 x 1 = 24.
Step 7: Calculate 2! which is 2 x 1 = 2.
Step 8: Divide the total arrangements: 24 / 2 = 12.
Step 9: Conclude that there are 12 different ways to arrange the letters of the word 'BOOK'.

Permutations with Repetition – The concept of calculating arrangements of letters where some letters are repeated, using the formula n! / (p1! * p2! * ... * pk!) where n is the total number of items and p1, p2, ..., pk are the frequencies of the repeated items.