What is the probability that a phone number generated using the digits
1, 2, 2, 4, 5, 5, 6, and 2 is the number 654-5222?
mmm
\(\frac{1}{8}\times \frac{2}{7}\times \frac{1}{6}\times \frac{1}{5}\times \frac{3}{4}\times \frac{2}{3}\times \frac{1}{2}\\ =\frac{1*2*1*1*3*2*1}{8!}\\ =\frac{12}{40320}\\ =\frac{1}{336}\\\)
OR
The number of permutations for choosing 7 digits from these digits is
\(\frac{8P7}{3P3*2P2}=\frac{8!}{3!2!}=\frac{40320}{6*2}=336\)
We want the probability of choosing just one of these permutations so the answer is \(\frac{1}{336}\)
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