In how many ways can the letters of the word 'LEVEL' be arranged?
Practice Questions
Q1
In how many ways can the letters of the word 'LEVEL' be arranged?
60
30
20
40
Questions & Step-by-Step Solutions
In how many ways can the letters of the word 'LEVEL' be arranged?
Correct Answer: 30
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.
