Final answer:
To find the number of different selections possible for presenting four different awards to a class of 20 students, where each can receive only one award, we calculate the permutations: 20 x 19 x 18 x 17, resulting in 116,280 different selections.
Step-by-step explanation:
The question asks how many different selections are possible when presenting four different awards to students in a class of 20, with each student able to receive at most one award. This can be solved using the concept of permutations.
Starting with the first award, there are 20 students eligible. Once the first award is given, there are 19 students left for the second award, then 18 for the third, and finally 17 for the forth. The number of different selections possible is the product of these numbers.
Therefore, the total number of different combinations is 20 × 19 × 18 × 17 which equals 116,280 different selections.