Question

You pick 4 digits (0-9) at random without replacement, and write them in the order picked.

What is the probability that you have written the first 4 digits of your phone number? Assume there are no repeats of digits in your phone number.

Give your answer as a fraction.

Please circle the answer

Answer 1

Answer:

Probability that I have written the first 4 digits of my phone number =

= 1 / Total number of ways that the 4 digits could be taken out and arranged in a line.

Let those 4 digits be represented as:

Now for each blank we are picking up a digit. There are 10 possibilities for the first blank as we have 10 digits to choose from that is 0 to 9. For second blank we have only 9 choices left and so on...

Therefore the total number of ways to select 4 digits and arrange then in a line would be:

10 p 4 = 10! / (10-4)! = 10! / 6! = 5040

Therefore the required probability that I have written the first 5 digits of my phone number = 1 / 5040