Question

At the end of each 6 weeks of study, a math class with 18 students selects one student to win each of four awards: most creative problem solver, most proficient using the handheld, most diligent, and most improved. No student can receive the same award twice, and any student can be honored in at most one way in any given 6 weeks. At the end of the first 6 weeks, in how many possible ways could the awards be given? At the end of each 6 weeks of study, a math class with 18 students selects one student to win each of four awards: most creative problem solver, most proficient using the handheld, most diligent, and most improved. No student can receive the same award twice, and any student can be honored in at most one way in any given 6 weeks. At the end of the first 6 weeks, in how many possible ways could the awards be given?

Answer 1

There are 18 students in the math class and 4 awards to be given at the end of the first 6 weeks. No student can receive the same award twice, and any student can be honored in at most one way in any given 6 weeks. The total number of possible ways the awards can be given is 73440.

Step-by-step explanation:

There are 18 students in the math class and 4 awards to be given at the end of the first 6 weeks. No student can receive the same award twice, and any student can be honored in at most one way in any given 6 weeks.

For the first award, any of the 18 students can be chosen. So there are 18 possibilities for the first award.

For the second award, after one student has been chosen for the first award, there are now 17 students remaining. So there are 17 possibilities for the second award.

Similarly, after 2 students have been chosen for the first two awards, there are now 16 students remaining for the third award, and 16 possibilities.

Finally, after 3 students have been chosen for the first three awards, there are now 15 students remaining for the fourth award, and 15 possibilities.

Therefore, the total number of possible ways the awards can be given is: 18 * 17 * 16 * 15 = 73440