In how many ways can the letters of the word 'LEVEL' be arranged?
Practice Questions
1 question
Q1
In how many ways can the letters of the word 'LEVEL' be arranged?
60
30
20
40
The word 'LEVEL' has 5 letters with 'L' and 'E' repeating. The arrangements = 5! / (2! * 2!) = 30.
Questions & Step-by-step Solutions
1 item
Q
Q: In how many ways can the letters of the word 'LEVEL' be arranged?
Solution: The word 'LEVEL' has 5 letters with 'L' and 'E' repeating. The arrangements = 5! / (2! * 2!) = 30.
Steps: 8
Step 1: Count the total number of letters in the word 'LEVEL'. There are 5 letters: L, E, V, E, L.
Step 2: Identify the repeating letters. In 'LEVEL', the letter 'L' appears 2 times and the letter 'E' also appears 2 times.
Step 3: Use the formula for arrangements of letters with repetitions. The formula is: Total arrangements = Total letters! / (Repeating letters1! * Repeating letters2!).
Step 4: Plug in the values into the formula. We have 5 letters total, and 2 L's and 2 E's. So, it becomes: 5! / (2! * 2!).
Step 5: Calculate 5!. This is 5 x 4 x 3 x 2 x 1 = 120.
Step 6: Calculate 2!. This is 2 x 1 = 2. Since we have two repeating letters, we need to calculate (2!)^2 = 2 x 2 = 4.
Step 7: Now divide the total arrangements by the product of the factorials of the repeating letters: 120 / 4 = 30.
Step 8: Therefore, the total number of ways to arrange the letters of the word 'LEVEL' is 30.
