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prealgebra intermediate

Problem

Megan has lost Fatima's phone number. Megan knows that the first three digits are either 296 or 299. The remaining four digits are 0, 1, 6 and 7, but she isn't sure of the order of these digits. If Megan randomly dials a seven-digit number that meets these conditions, what is the probability that she dials Fatima's correct number? Express your answer as a common fraction.
Solution
There are 2 different ways in which Megan can type the first three numbers. There are different orderings of the digits 0, 1, 6 and 7 for the last four digits. So, there are different numbers she can dial. Since exactly one number will be Fatima's, there is a probability of Megan guessing it right.
Final answer
\frac{1}{48}