Discussion

How many 3-letter words can be formed out of the letters of the word ‘CORPORATION’, if repetition of letters is not allowed?

Answer: B

CORPORATION has eleven letters, but repetition of letters is not allowed in the word formed, so only the distinct letters may be used:

\[ C,\ O,\ R,\ P,\ A,\ T,\ I,\ N \rightarrow 8 \text{ distinct} \]

Order matters in a word, so this is a permutation:

\[ {}^{8}P_{3} = 8 \times 7 \times 6 = 336 \]

The repeated O's and R's contribute nothing extra, since no letter may be used twice.

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