Given the set (1,2,3,4,5) how many 3-digit numbers can be formed if the first digit is 5 and no digit is repeated?
To find the number of 3-digit numbers that can be formed with the given conditions, we can break down the problem into three steps:
Step 1: Determine the possible digits for each position
Since the first digit must be 5, we don't have any other options.
For the second digit, we have four remaining digits available (1, 2, 3, 4). However, since no digit can be repeated, we have three options left after using one digit for the second position.
For the third digit, we have three remaining digits available (one digit was used for the first position, and one digit was used for the second position). Again, since no digit can be repeated, we have two options left after using two digits for the first two positions.
Therefore, the possible digits for each position are:
First digit: 5
Second digit: 3 options (1, 2, 4)
Third digit: 2 options (3, 4)
Step 2: Multiply the number of options for each position
To find the total number of 3-digit numbers that can be formed, we need to multiply the number of options for each position:
Option for the first digit * Options for the second digit * Options for the third digit
Total = 1 * 3 * 2 = 6
There are six 3-digit numbers that can be formed if the first digit is 5 and no digit is repeated.
These numbers are:
513, 514, 523, 524, 533, 534