Question

Alex must choose a 4-digit code for a PIN number from the digits 1 through 9, without repeating any digits. What is the probability that the selected code:
a) is “1234”
b) starts with a “1”
c) contains a “1” in any position

Answer 1

looking for help

Answer 2

The total # of different combinations is 9 x 8 x 7 x 6. So for question a), you have:

1/(9 x 8 x 7 x 6)

The number of combinations that start with a "1" is 1 x 8 x 7 x 6. So, for question b), you have:

(8 x 7 x 6)/(9 x 8 x 7 x 6) = 1/9

Answer 3

For c), the number of combinations that have a "1" anywhere in it is:

1 x 8 x 7 x 6 + 8 x 1 x 7 x 6 + 8 x 7 x 1 x 6 + 8 x 7 x 6 x 1 or
4(8 x 7 x 6)

So, you would have:

4(8 x 7 x 6) / (9 x 8 x 7 x 6) = 4/9

Answer 4

I really appreciate that thnx so much

Answer 5

You're quite welcome! Good luck in your studies!