Question

A 5-digit combination lock with digits 0-9 can be opened only if a correct combination of digits is chosen. Find the probability of guessing the correct combination if:

A. no digit is repeated

B. digits can repeat and zero is not one of the digits in the combination

(Can this be done in fraction form? Thanks!)

Answer 1

A. 5 digit code with digits from 0-9 with no repetition.

Choices for 1st digit=10, and choices for successive digits are 9,8,7,6.

Probability of guessing it correctly on first try is

1/(10*9*8*7*6) = 1/30240

B. If zero is not in the combinations, then the domain of digits is 1-9, or 9 choices. Digits can repeat means every digit in the code has 9 choices.

Number of arrangements = 9^5 = 59049

Probability of guessing at first try = 1/59049

Answer 2

A.
$|\Omega|=10\cdot9\cdot8\cdot7\cdot6=30240\\ |A|=1\\\\ P(A)=\dfrac{1}{30240}$

B.
$|\Omega|=9^5=59049\\ |A|=1\\\\ P(A)=\dfrac{1}{59049}$