Questions: How many different three-digit numbers can be formed using the digits 5,8,3,1, and 9 without repetition? For example, 883 is not allowed. The number of different three-digit numbers is

How many different three-digit numbers can be formed using the digits 5,8,3,1, and 9 without repetition? For example, 883 is not allowed.

The number of different three-digit numbers is

Transcript text: How many different three-digit numbers can be formed using the digits $5,8,3,1$, and 9 without repetition? For example, 883 is not allowed. The number of different three-digit numbers is $\square$

Solution

Solution Steps

Step 1: Identify the total number of digits available

The digits available are $5, 8, 3, 1,$ and $9$. There are $5$ distinct digits.

Step 2: Determine the number of positions in the three-digit number

A three-digit number has three positions: hundreds, tens, and units.

Step 3: Calculate the number of choices for each position

For the hundreds place, any of the $5$ digits can be used.
For the tens place, one digit has already been used, so there are $4$ remaining choices.
For the units place, two digits have already been used, so there are $3$ remaining choices.

Step 4: Multiply the number of choices for each position

The total number of different three-digit numbers is: \[ 5 \times 4 \times 3 = 60 \]