Try this beautiful Combination Problem based on Non-negative integer solutions from PRMO 2016.
There are three kinds of fruits in the market. How many ways are there to purchase 25 fruits from among them if each kind has at least 25 of its fruit available?
Permutation and combination
Non negative integer solution to an equation
Maximum possible value of variable
Excursion in Mathematics
PRMO 2016
351
The given problem can be expressed in terms of the following equation
$x_1 + x_2 + x_3 = 25$
where $ x_!, x_2, x_3$ are the number of different fruits brought
The solution of the problem is equivalent to finding the non-negative integer solution to this given equation
Try to relate it to the following idea:
There are 25 balls and 2 sticks arranged in a straight line. We want to find the number of different arrangements possible. To the the different possible distinct arrangement we may apply permutation with repetition
