Question

A small combination lock on a suitcase has 5 ​wheels, each labeled with the 10 digits from 0 to 9. If an opening combination is a particular sequence of 5 digits with no​ repeats, what is the probability of a person guessing the right​ combination?

Answer 1

Answer:  The required probability is 0.3.

Step-by-step explanation:  Given that a small combination lock on a suitcase has 5 ​wheels, each labeled with the 10 digits from 0 to 9.

An opening combination is a particular sequence of 5 digits with no​ repeats.

We are to find the probability of a person guessing the right​ combination.

If the 5 digits do no repeat, then we have

10 options for first digit, 9 options for second digit, 8 options for third digit, 7 options for fourth digit and 6 options for fifth digit.

Let A denote the event that the combination is a particular sequence of 5 digits with no​ repeats.

Also, let S be the sample space for the experiment.

Then, we have

$n(A)=10\times9\times8\times7\times6=30240,\\\\n(S)=10^5=100000.$

Therefore, the probability of even A is given by

$P(A)=\dfrac{n(A)}{n(S)}=\dfrac{30240}{100000}=0.3.$

Thus, the required probability is 0.3.