How many different ways can the letters of the word 'LEVEL' be arranged?

How many different 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.
Step 2: Identify if there are any 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 numbers into the formula. We have 5 letters, with 'L' repeating 2 times and 'E' repeating 2 times: 5! / (2! * 2!).
Step 5: Calculate 5! which is 5 x 4 x 3 x 2 x 1 = 120.
Step 6: Calculate 2! which is 2 x 1 = 2. Since 'L' and 'E' both repeat, we need to calculate (2! * 2!) = 2 * 2 = 4.
Step 7: Now divide the total arrangements by the repeating arrangements: 120 / 4 = 30.
Step 8: Therefore, the number of different ways to arrange the letters of the word 'LEVEL' is 30.

Permutations of Multisets – The arrangement of letters in a word where some letters are repeated, calculated using the formula n! / (n1! * n2! * ... * nk!)