In how many ways can the letters of the word 'SCHOOL' be arranged?
Practice Questions
1 question
Q1
In how many ways can the letters of the word 'SCHOOL' be arranged?
720
360
480
600
The word 'SCHOOL' has 6 letters with 'O' repeating 2 times. The arrangements are 6! / 2! = 360.
Questions & Step-by-step Solutions
1 item
Q
Q: In how many ways can the letters of the word 'SCHOOL' be arranged?
Solution: The word 'SCHOOL' has 6 letters with 'O' repeating 2 times. The arrangements are 6! / 2! = 360.
Steps: 7
Step 1: Count the total number of letters in the word 'SCHOOL'. There are 6 letters: S, C, H, O, O, L.
Step 2: Identify if any letters are repeated. The letter 'O' appears 2 times.
Step 3: Use the formula for arrangements of letters where some letters are repeated. The formula is: Total arrangements = Total letters! / (Repeated letters!)
Step 4: Calculate the total arrangements. Here, it is 6! (for 6 letters) divided by 2! (for the 2 O's).
Step 5: Calculate 6! which is 720 and 2! which is 2.
Step 6: Divide 720 by 2 to get the final number of arrangements: 720 / 2 = 360.
Step 7: Conclude that there are 360 different ways to arrange the letters of the word 'SCHOOL'.
