How many ways to distribute M mangoes among n people?

Given m and n representing number of mangoes and number of people respectively. Task is to calculate number of ways to distribute m mangoes among n people. Considering both variables m and n, we arrive at 4 typical use cases where mangoes and people are considered to be:

How do you calculate the number of identical mangoes?

So we need ways to calculate our answer. As all the mangoes are considered to be identical, we divide by to deduct the duplicate entries. Similarly, we divide the above expression again by because all people are considered to be identical too. // no of ways to distribute m.

How many mangoes are there in the population total?

Even though ‘population’ could refer to items or objects for statistical purposes, if the population total actually refers to mangoes (100) then the number of people would have to come from the further distribution description of 1 man, 1 woman and 4 children (total 6 persons).

How do you arrange m mangoes and n-1 partitioners?

In this case we need to arrange m mangoes and n-1 partitioners all together. So we need ways to calculate our answer. As all the mangoes are considered to be identical, we divide by to deduct the duplicate entries. Similarly, we divide the above expression again by because all people are considered to be identical too.

How many ways 4 objects can be divided in two groups?

Eg3: In how many ways 4 objects can be divided in two groups such that each group contains 2 objects each. Solution: According to the above discussion the number of ways of division is 4! Will be in numerator and two times 2! will be in denominator as we made two groups of group size 2 objects.

What is a distinctdistinct objects into distinct bins?

Distinct objects into distinct bins is a type of problem in combinatorics in which the goal is to count the number of possible distributions of objects into bins. A distribution of objects into bins is an arrangement of those objects such that each object is placed into one of the bins. In this type of problem, the objects and bins are distinct.

What is a distribution of objects into bins?

A distribution of objects into bins is an arrangement of those objects such that each object is placed into one of the bins. In this type of problem, the objects and bins are distinct.