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# PRMO 2016 Problem No 4 | Combination Problem

Try this beautiful Combination Problem based on Non-negative integer solutions from PRMO 2016.

## Combination Problem - PRMO 2016 Problem 4

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?

### Key Concepts

Permutation and combination

Non negative integer solution to an equation

Maximum possible value of variable

## Suggested Book | Source | Answer

Excursion in Mathematics

PRMO 2016

351

## Try with Hints

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

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Try this beautiful Combination Problem based on Non-negative integer solutions from PRMO 2016.

## Combination Problem - PRMO 2016 Problem 4

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?

### Key Concepts

Permutation and combination

Non negative integer solution to an equation

Maximum possible value of variable

## Suggested Book | Source | Answer

Excursion in Mathematics

PRMO 2016

351

## Try with Hints

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

## Subscribe to Cheenta at Youtube

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