Understanding the Problem
When dividing 15 mangoes among three students equally, we want to find the number of ways to distribute these mangoes so that each student receives the same number. Since we have 15 mangoes and 3 students, each student will get 5 mangoes.
Distribution of Mangoes
- Each student must receive exactly 5 mangoes.
- This can be viewed as a combinatorial problem where we need to select 5 mangoes for the first student, 5 for the second, and the remaining 5 automatically go to the third student.
Calculating the Combinations
To find the number of ways to choose 5 mangoes for the first student from 15:
- The first selection (for Student 1) can be done in C(15, 5) ways.
- The next selection (for Student 2) is from the remaining 10 mangoes. This can be done in C(10, 5) ways.
- The last 5 mangoes go to Student 3, which is done in C(5, 5) ways (which equals 1).
Adjusting for Overcounting
Since the order of selection does not matter (i.e., giving 5 mangoes to Student 1, then Student 2, and finally Student 3 is the same as giving them in a different order), we must divide by the number of ways to arrange the 3 students, which is 3! (factorial of 3).
Final Calculation
Thus, the total number of ways to distribute the mangoes is given by:
- Total Ways = (C(15, 5) * C(10, 5) * C(5, 5)) / 3!
This gives you the number of unique distributions of the 15 mangoes among the three students, ensuring that each receives an equal share.