Question on: JAMB Mathematics - 2023
How many different 8 letter words are possible using the letters of the word SYLLABUS?
A
(8 - 1)!
B
\(\frac{8!}{2!}\)
C
\(\frac{8!}{2! 2!}\)
D
8!
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Correct Option: C
To find the number of different 8-letter words using the letters of the word "SYLLABUS," we can use the formula for permutations of a multiset, where some elements are repeated.
The correct formula is:
\[ \frac{8!}{2! \cdot 2!} \]
This is because there are 8 positions, but the letter "S" appears twice, and the letter "L" appears twice. So, we divide by \(2!\) for each repeated letter to correct for the overcounting.
Therefore, the correct answer is \(\frac{8!}{2! \cdot 2!}\)
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