Question

Susan has a combination lock that requires a 5 number sequence. The numbers on the lock range from one to thirty-five. What is the probability that her sequence of numbers is 12345? What is the probability that her sequence of numbers is five numbers of the same value?

Answer 1

Question 1)

Number of digits the Combination lock uses = 35
Number sequence for the lock is made from 5 numbers.

Since each number position on the lock can take any number from 1 to 35 without any restriction, the number of combination sequences of 5 digits will be equal to 35 x 35 x 35 x 35 x 35

Thus, the total number of 5 digit sequences = 35⁵ = 52521875

The sequence 12345 is only one sequence out of 52521875 possible sequences. 

So, the probability that her sequence of numbers is 12345 = $\frac{1}{52521875}$

Question 2)
Total number of possible sequences = 52521875

Sequence of numbers with 5 numbers of the same value will be of the form:

11111
22222
33333
and so on

Since the number of digits are upto 35, there can be 35 such sequences with same five digits in the entire sequence.

So the probability that her sequence of numbers is five numbers of the same value = $\frac{35}{52521875}= \frac{1}{1500625}$