How many different ways can you arrange the letters in the word 'SCHOOL'?

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Question: How many different ways can you arrange the letters in the word \'SCHOOL\'?

Options:

Correct Answer: 360

Solution:

The number of arrangements of the letters in \'SCHOOL\' is 6! / 2! = 360.

How many different ways can you arrange the letters in the word 'SCHOOL'?

How many different ways can you arrange the letters in the word 'SCHOOL'?

Step 1: Count the total number of letters in the word 'SCHOOL'. There are 6 letters: S, C, H, O, O, L.
Step 2: Identify if there are any repeating letters. In 'SCHOOL', the letter 'O' appears 2 times.
Step 3: Use the formula for arrangements of letters, which is total letters factorial divided by the factorial of the number of repeating letters.
Step 4: Calculate the total arrangements: 6! (which is 6 x 5 x 4 x 3 x 2 x 1) equals 720.
Step 5: Calculate the arrangements for the repeating letter 'O': 2! (which is 2 x 1) equals 2.
Step 6: Divide the total arrangements by the arrangements of the repeating letters: 720 / 2 = 360.
Step 7: Therefore, the number of different ways to arrange the letters in 'SCHOOL' is 360.

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