A five digit code using numbers from 1 to 6 is used for remote access to voicemail. Determine the probability that a randomly selected code has the same first 2 digits.

Question

A five digit code using numbers from 1 to 6 is used for remote access to voicemail. Determine the probability that a randomly selected code has the same first 2 digits.

I am not sure the answer may be 1/6 or 1/36..

Please explain this !!!! Thanks!

Answer 1

Well we can select the code in 6 x 6 x 6 x 6 x 6 = 7776 ways

If the first two digits are the same, we can select the first two digits in 6 ways (11, 22, ... 66) and the other 3 digits in 6 x 6 x 6 ways.

So total ways = 4 x 6 x 6 x 6 = 864 ways

So probability = 864 / 7776 = 1/9