To determine how many different ways we can select the first and second students in a spelling bee with 10 participants, we can use the concept of permutations.
When we are choosing the first student, we have 10 options (since there are 10 students). After selecting the first student, we have 9 remaining students to choose from for the second position.
The number of ways to choose the first and second students can therefore be calculated as follows:
- Ways to choose the first student: 10
- Ways to choose the second student after the first has been chosen: 9
The total number of combinations is the product of these two values:
Total ways = 10 (first choice) × 9 (second choice) = 90
Thus, there are 90 different ways to choose the first and second students in the spelling bee.