Question

Please help I'm struggling in math

A teacher's Web site requires a password that is 5 digits long with no digits repeated. The teacher uses a computer program to produce 5-digit password and distributes them randomly to the students. What is the probability that a student will receive a 5-digit password of consecutive numbers in increasing order?

Answer 1

Writing out some of the possible outcomes might help us visualize what's happening here.
Every digit must be unique, and every digit must be only 1 greater than the preceding digit.

Were we to start with the digit 1, the next could be 2, the next 3, the next 4, and the last 5.
{2,3,4,5,6} would be another "OK" password.

(3, 2, 1, 4, 5} would be unacceptable.

{0, 1, 2, 3, 4} would be acceptable.

What would the total number of possible outcomes be (realizing that some of them would not be acceptable passwords)? Before attempting to answer: think: up front there'd be 10 digits to choose from, then 9, then 8, then 7 and then 6, since we do not replace any digit drawn.

Hope these facts / questions help you get started out.

Answer 2

Another question to ponder: How many possible combinations of 10 digits taken 5 at a time are there?

Yet another question: Should we be thinking in terms of permutations instead of combinations, since order DOES matter in this password problem?

Answer 3

permentation @mathmale

Answer 4

Lisa, the word is "permutation" (or "permutations," in the plural).

You might get some helpful info from this web site:

http://www.mathsisfun.com/combinatorics/combinations-permutations.html