Question

How many different three-digit numbers can be written using digits from the set 5, 6, 7, 8, 9 without any repeating digits?

Answer 1

Answer: 60 different numbers can be formed

Step-by-step explanation:

Note that we have 5 different digits, and we must select 3 of them. They should not be repeated

The order of selection is important in this case, because the number 532 is not the same as the number 235.

So we have a permutations problem, where we have a set of n elements and we want to choose r from them.

Then we define the permutacion as:

$nPr=\frac{n!}{(n-r)!}$

In this case note that n=5 because there are 5 elements in the set.

r = 3 because we combine the elements to form three-digit numbers

Then:

$5P2=\frac{5!}{(5-3)!}$

$5P2=\frac{5!}{2!}$

$5P2=\frac{5*4*3*2!}{2!}$

$5P2=5*4*3$

$5P2=60$