03EasyExact AnswerBasic ProbabilityIn 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?
Question
03EasyExact AnswerBasic ProbabilityIn 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?
Solution
This is a permutation problem. The number of ways to arrange n items taken r at a time is given by the permutation formula:
P(n, r) = n! / (n-r)!
where:
- n is the total number of items
- r is the number of items to arrange
- "!" denotes factorial, which is the product of all positive integers up to that number
In this case, we have 5 teachers and 3 students, so we want to find the number of ways to arrange 5 teachers taken 3 at a time.
So, we calculate:
P(5, 3) = 5! / (5-3)! = 60
So, there are 60 ways the five teachers can be allocated to these three students.
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