There are 39 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?39!36!3!36!3!39! 39!36!36!39! 39!39!36!36!
Question
There are 39 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?39!36!3!36!3!39! 39!36!36!39! 39!39!36!36!
Solution
The problem is asking for the number of ways to choose 3 students out of 39 to receive an award. This is a combination problem, not a permutation problem, because the order in which the students are chosen does not matter.
The formula for combinations is:
C(n, r) = n! / [r!(n-r)!]
where:
- n is the total number of items,
- r is the number of items to choose,
- "!" denotes factorial, which is the product of all positive integers up to that number.
So, in this case, n = 39 (the total number of students) and r = 3 (the number of students to receive an award).
Substituting these values into the formula gives:
C(39, 3) = 39! / [3!(39-3)!]
Calculating the factorials and simplifying gives:
C(39, 3) = 393837 / (321) = 9139
So, there are 9139 possible ways for the students to be awarded.
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