Question

you pick 7 digits (0 - 9) at random without replacement, and write them in the order picked. what is the probability that you have written the first 7 digits of your phone number? assume there are no repeats of digits in your phone number. give your answer as a fraction.

Explanation:

Step1: Calculate number of permutations

The number of ways to pick 7 non - repeating digits out of 10 digits (0 - 9) in order is given by the permutation formula $P(n,r)=\frac{n!}{(n - r)!}$, where $n = 10$ and $r=7$. So $P(10,7)=\frac{10!}{(10 - 7)!}=\frac{10!}{3!}=10\times9\times8\times7\times6\times5\times4 = 604800$.

Step2: Determine favorable outcomes

There is only 1 favorable outcome, which is the first 7 digits of the phone number.

Step3: Calculate probability

The probability $P$ is the number of favorable outcomes divided by the number of total outcomes. So $P=\frac{1}{604800}$.

Answer:

$\frac{1}{604800}$