In how many ways can the letters of the word 'SCHOOL' be arranged?
Practice Questions
Q1
In how many ways can the letters of the word 'SCHOOL' be arranged?
720
360
480
600
Questions & Step-by-Step Solutions
In how many ways can the letters of the word 'SCHOOL' be arranged?
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'.
