how many two-digit numbers can be formed from the digits 1, 2, 3, 4, 5

Question

1.How many two-digit numbers can be

formed from the digits 1, 2, 3, 4, 5 if

repetition is

a) permitted?

b) not permitted?

an explanation would be great for a better understanding, thanks!

Answer 1

(a) 1st digit can be chosen in 5 ways and second in 5 ways (as repetition is permitted), so 5 x 5 = 25 two digit numbers

(b) 1st can be chosen in 5 ways, and second in 4 (as 1 digit has been used and repetition isn't possible), so 5x4 = 20 two digit numbers

You can list out the possibilities to check these if you wish