Find the number of permutations of the letters of the word SCHOOL.

Analysis

To find the number of permutations of the letters in the word SCHOOL, we need to determine the total number of letters and identify if any letters are repeated.

Concept

The number of permutations of $n$ objects, where some objects are identical, is given by the formula:

Where:

• $n$ is the total number of items.
• $n!$ (n factorial) is the product of all positive integers up to $n$.
• $p!, q!$ represent the factorials of the counts of each repeated item.

Solution

1. Count the total letters: The word SCHOOL has 6 letters ($n = 6$).
2. Identify repetitions: • S: 1 • C: 1 • H: 1 • O: 2 • L: 1 • The letter 'O' appears twice.
3. Apply the formula: $$\text{Permutations} = \frac{6!}{2!}$$
4. Calculate the values: • $6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720$ • $2! = 2 \times 1 = 2$ • $\text{Permutations} = \frac{720}{2} = 360$

Conclusion

The total number of distinct arrangements for the letters in the word SCHOOL is 360.

Exam Tip: Always remember to divide by the factorial of the number of times a letter repeats. If you forget to divide by the repetitions, you will get 720, which is a common distractor in JAMB questions!