Question

Write a program for mango distribution in c language

Answer 1

Answer:

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:

1) Both identical

2) Unique and identical respectively

3) Identical and unique respectively

4) Both unique

amongst n identical people

If we try to spread m mangoes in a row, our goal is to divide these m mangoes among n people sitting somewhere between arrangement of these mangoes. All we need to do is pool these m mangoes into n sets so that each of these n sets can be allocated to n people respectively.

To accomplish above task, we need to partition the initial arrangement of mangoes by using n-1 partitioners to create n sets of mangoes. In this case we need to arrange m mangoes and n-1 partitioners all together. So we need

(m+ n-1)! ways to calculate our answer.

Illustration given below represents an example(a way) of an arrangement of partitions created after placing 3 partitioners namely P1, P2, P3 which partitioned all 7 mangoes into 4 different partitions so that 4 people can have their own portion of respective partition:

Example of an arrangement after partitioning

As all the mangoes are considered to be identical, we divide

(m+n-1)! by

(m)! to deduct the duplicate entries. Similarly we divide the above expression again by

(n-1)! because all people are considered to be identical too.

The final expression we get is :

(m+n-1)!/((n-1)!*(m)!)

The above expression is even-actually equal to the binomial coefficient:

^m^+^n^-^1C_n_-_1

Example:

Input : m = 3, n = 2

Output : 4

There are four ways

3 + 0, 1 + 2, 2 + 1 and 0 + 3

Input : m = 13, n = 6

Output : 8568

Input : m = 11, n = 3

Output : 78

Explanation:

hope it will help you

Answer 2

Explanation:

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