The number of 4-letter words, with or without meaning, which can be formed using the letters PQRPRSTUVP, is:

Question

Accepted Answer

Given: The letters are PQRPRSTUVP.

Find: The number of $4$ -letter words that can be formed.

The solution lists the letter frequencies as P(3), R(2), Q(1), S(1), T(1), U(1), V(1) and states the final answer as $1230$ , but this disagrees with the recorded correct answer $1422$ . So the extracted working is inconsistent with the declared answer.

From the provided working, the cases counted are:

$3$ alike and $1$ different

1 \times \binom{6}{1} \times \frac{4!}{3!} = 24

$2$ alike and $2$ alike

\binom{2}{2} \times \frac{4!}{2!2!} = 6

$2$ alike and $2$ different

2 \times \binom{6}{2} \times \frac{4!}{2!} = 360

All $4$ different

\binom{7}{4} \times 4! = 840

Adding the values shown in the solution,

24 + 6 + 360 + 840 = 1230

However, the solution's explicitly marks the correct answer as $1422$ . Therefore, the extracted solution content is contradictory, and the accepted answer from the source is $1422$ .

Given: The page provides both a declared correct answer and a worked solution.

Find: Which value should be recorded.

The worked steps end with $1230$ , while the solution says Correct Answer: $1422$ .

Under answer resolution, when the available worked solution is internally inconsistent with the declared answer, the discrepancy must be preserved in the solution text rather than hidden. Hence the recorded answer is taken as $1422$ , with the mismatch explicitly noted.

Therefore, the accepted numerical answer is $1422$ .

Answer

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