Question

The digits 1-5 are used for a set of locker codes. Suppose the digits cannot repeat. Find the number of possible two digit and three digit codes. Describe any pattern and use it to predict the number of possible five digit codes.

Answer 1

so you would do
5×4×3= 60
and
5×4=20
so, for a 3 digit code there are 60 possibilities and for a 2 digit code there are 20 possibilities.

Answer 2

Answer: Number of possible two digit codes= 20

Number of possible three digits code = 60

To make five digit codes the pattern will be given by using permutations:-

`^5P_5=(5!)/((5-5)!)`

Number of possible five digit codes =120

Explanation:

Given: The number of digits used for a set of locker codes =5

If repetition is not allowed, then the number of possible two digit codes is given by by using permutations:-

`^5P_2=(5!)/((5-2)!)=(5*4*3!)/(3!)=20`

Similarly, the number of possible three digit codes is given by :-

`^5P_3=(5!)/((5-3)!)=(5*4*3*2!)/(2!)=60`

Similarly, to make five digit codes the pattern will be given by using permutations:-

`^5P_5=(5!)/((5-5)!)`

Therefore, the number of possible five digit codes =
`(5!)/((5-5)!)=5!=120`