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:-
[tex]^5P_5=\frac{5!}{(5-5)!}[/tex]
Number of possible five digit codes =120
Step-by-step 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:-
[tex]^5P_2=\frac{5!}{(5-2)!}=\frac{5\times4\times3!}{3!}=20[/tex]
Similarly, the number of possible three digit codes is given by :-
[tex]^5P_3=\frac{5!}{(5-3)!}=\frac{5\times4\times3\times2!}{2!}=60[/tex]
Similarly, to make five digit codes the pattern will be given by using permutations:-
[tex]^5P_5=\frac{5!}{(5-5)!}[/tex]
Therefore, the number of possible five digit codes =[tex]\frac{5!}{(5-5)!}=5!=120[/tex]
