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

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

Step 1: Count the total number of letters in the word 'LEVEL'. There are 5 letters: L, E, V, E, L.
Step 2: Identify any repeated letters. In 'LEVEL', the letter 'E' 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 5! (for 5 letters) divided by 2! (for the 2 E's).
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.
Step 7: Divide the total arrangements by the repeated arrangements: 120 / 2 = 60.
Step 8: The final answer is 30, which is the number of unique arrangements of the letters in 'LEVEL'.

Permutations of Multisets – The concept of arranging letters where some letters are repeated, requiring the use of factorials to account for indistinguishable items.