Question

How many 2 - digit numbers can be formed from the digits {1, 2, 3, 4, 5} without repetition and with repetition?

Answer 1

Forming a 2-digit number is same as finding the $2$-digit number and also it includes the arrangement of numbers.

So, we can get the number of ways to form $2$-digit number from the given set by using permutation.

Here, we have $5$ digits and we need to choose $2$-digits.

Then, the number of $2$-digit numbers formed from the given set without repetition is ${}^5{P}_2=\frac{5!}{(5-2)!}=\frac{5!}{3!}=20$

The numbers formed by repetition are $\{11,22,33,44,55\}$

$\therefore$ The number of $2$-digit numbers formed from the given set with repetition $={}^5{P}_2+5=20+5=25$