Question

How many different three-digit numbers can be written using digits from the set 5, 6, 7, 8, 9 without any repeating digits?A. 625B. 20C. 120D. 60

Answer 1

Given:

The given numbers are 5,6,7,8,9.

Required:

Find the way so three-digit numbers can be written using digits from the sets 5, 6, 7, 8, 9 without any repeating digits.

Step-by-step explanation:

Let n is the total number then the way to write m digits number is given by the formula:

`A(n,m)=(n!)/((n-m)!)`

So the way to write 3 digits numbers are:

`\begin{gathered} A(5,3)=(5!)/((5-3)!) \\ =(5!)/(2!) \\ =5*4*3 \\ =60 \end{gathered}`

Final Answer:

Option D is the correct answer.