A teacher wants to award prizes for 1st,2nd, 3rd,4th, and 5th in a class of 30. In how many ways can the prizes be awarded (assume no two students tie)?

There are 30 students in the class, so for the first prize, there are 30 choices. For the second prize, there are 29 choices left. For the third prize, there are 28 choices left, and so on.

Therefore, the total number of ways the prizes can be awarded is:

30 * 29 * 28 * 27 * 26 = 17,748,480

So, there are 17,748,480 ways the prizes can be awarded in a class of 30 students.

Step 1: Determine the total number of possible arrangements

There are 30 students in the class. For each prize, there are 30 possible students who could win.

Step 2: Multiply the number of possible arrangements for each prize

For 1st prize, there are 30 possible students.
For 2nd prize, there are 29 possible students (since one student has already won first prize).
For 3rd prize, there are 28 possible students.
For 4th prize, there are 27 possible students.
For 5th prize, there are 26 possible students.

Step 3: Multiply the results together

30 - 29 - 28 - 27 - 26 = 14,732,640

Therefore, there are 14,732,640 possible ways to award the prizes in a class of 30 without any ties.