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!
Question
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!
Solution
The number of ways the students can be awarded is calculated using the formula for permutations of a subset:
P(n, r) = n! / (n-r)!
where:
- n is the total number of students, which is 32
- r is the number of students to be awarded, which is 3
So, the number of ways the students can be awarded is:
P(32, 3) = 32! / (32-3)!
= 32! / 29!
This is the number of permutations of 32 students taken 3 at a time.
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