How many ways can you arrange the letters of the word 'BANANA'?

How many ways can you arrange the letters of the word 'BANANA'?

Step 1: Count the total number of letters in the word 'BANANA'. There are 6 letters.
Step 2: Identify the repeating letters. In 'BANANA', 'A' appears 3 times and 'N' appears 2 times.
Step 3: Use the formula for arrangements of letters with repetitions. The formula is total letters factorial divided by the factorial of each repeating letter's count.
Step 4: Write the formula: 6! / (3! * 2!).
Step 5: Calculate 6! (which is 720).
Step 6: Calculate 3! (which is 6) and 2! (which is 2).
Step 7: Multiply the factorials of the repeating letters: 3! * 2! = 6 * 2 = 12.
Step 8: Divide the total arrangements by the product of the repeating letters' factorials: 720 / 12 = 60.
Step 9: Conclude that there are 60 different ways to arrange the letters of the word 'BANANA'.

Permutations of Multisets – This concept involves calculating the number of distinct arrangements of letters in a word where some letters are repeated.