In how many ways can three awards be given to eight students under the following conditions? (See Example 6 in this section.)(a)if each student may receive more than one award

There are 32 students in a class. The class teacher announced that the first 3 students who completes a given project within two days will be awarded. What are the possible number of ways the students will be awarded?32!29!29!32!​ 32!29!3!29!3!32!​ 32!32!29!29!

Ten participants are participating in a competition. In how many ways can the first three prizes be won?Choices:- 920 620 720 850

6. At a recent dog show, there were 5 finalists. One of the finalists was awarded "Best in Show" and another finalist was awarded "Honorable Mention." In how many different ways could the two awards be given out?

In one school, there are five teachers: teacher A, teacher B, teacher C, teacher D and teacher E. However, only three students (Mr X, Mr Y and Mr Z) have entered the school this year. Note that in this school, one teacher is supposed to teach one student per teacher. In this case, how many ways can the five teachers be allocated to these three students?

In a running competition, a bronze, silver and gold medal must be given to the top three girls and top three boys. If 9 boys and 4 girls are competing, how many different ways could the six medals possibly be given out?