In how many ways can the letters of the word 'BOOK' be arranged? (2022)
Practice Questions
Q1
In how many ways can the letters of the word 'BOOK' be arranged? (2022)
12
24
16
8
Questions & Step-by-Step Solutions
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'.
