ProbabilityHardBloom L3
Question
A man sent 7 letters to his 7 friends. The letters are kept in the addressed envelopes at random. The probability that 3 friends receive correct letters and 4 letters go to wrong destinations is equal to
Options
A.$\frac{1}{8}$
B.$\frac{1}{16}$
C.$\frac{1}{24}$
D.$\frac{1}{4}$
Solution
Sol. [Key Concept: Man sends 7 letters at random: derangement-type probability.]
$$\begin{matrix} P & \ = \frac{\ ^{7}C_{3} \times 9}{7!} \\ & \ = \frac{1}{16} \end{matrix}$$
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