How many different ways can the letters of the word 'BOOK' be arranged? (2014)
Practice Questions
1 question
Q1
How many different ways can the letters of the word 'BOOK' be arranged? (2014)
12
24
36
48
The number of arrangements of the letters in 'BOOK' is 4! / 2! = 12.
Questions & Step-by-step Solutions
1 item
Q
Q: How many different ways can the letters of the word 'BOOK' be arranged? (2014)
Solution: The number of arrangements of the letters in 'BOOK' is 4! / 2! = 12.
Steps: 9
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' appears twice. This means we have repeating letters.
Step 4: To find the number of different arrangements, we use the formula for permutations of multiset: total letters factorial divided by the factorial of the number of times each letter repeats.
Step 5: Calculate the total arrangements using the formula: 4! (factorial of total letters) divided by 2! (factorial of the repeating letter 'O').
Step 6: Calculate 4! = 4 × 3 × 2 × 1 = 24.
Step 7: Calculate 2! = 2 × 1 = 2.
Step 8: Divide the total arrangements by the arrangements of the repeating letters: 24 / 2 = 12.
Step 9: Therefore, the number of different ways to arrange the letters of the word 'BOOK' is 12.
