Three students, Feng, Alexandra, and Gabriel, line up one behind the other. How many different ways can they stand in line?
There are 3 options for the first person in line, then 2 options left for the second person, and only 1 option left for the last person. Therefore, there are 3 x 2 x 1 = 6 different ways they can stand in line.
There are 3 students, so there are 3 choices for the first student in line. After the first student is chosen, there are 2 choices left for the second student. Finally, there is only 1 choice for the last student.
Multiplying the choices for each position gives us the total number of ways they can stand in line: 3 × 2 × 1 = 6 ways.
To find the number of different ways the three students can stand in line, we need to calculate the number of permutations.
Since there are 3 students, we start with 3 options for the first position. Once the first student is placed, we have 2 options left for the second position. Finally, for the last position, only 1 option is left.
So the total number of different ways the three students can stand in line is calculated as:
3 x 2 x 1 = 6
Therefore, there are 6 different ways the three students can stand in line.
To find the number of different ways they can stand in line, we need to determine the number of possible arrangements. Since there are three students, we can start by considering the first position in the line.
There are three choices for the first position (Feng, Alexandra, Gabriel). Once the first position is occupied, there are two choices remaining for the second position. Finally, after the first two positions are occupied, there is only one choice left for the third position.
Using the multiplication principle, we multiply these numbers together to get the total possible arrangements. So, the number of different ways they can stand in line is:
3 * 2 * 1 = 6
Therefore, there are 6 different ways they can stand in line.