Question

4 oranges are distributed among 4 friends named as Ankur, Parag, Milan and Deepak.
There are certain conditions for the distribution.
* If Ankur receives 1 orange then it is necessary to give 1-1 orange to all others.
* Parag has disagreed to receive 3 oranges.
* If Parag obtains 2 oranges then Ankur does not receive any orange.
* If Milan gets 3 oranges then Deepak gets 1 orange necessarily.
* Only Deepak can take all the 4 oranges.
How many methods are possible for the distribution of oranges?

Answer 1

Solution

4 orange to one person 4

3 to one and 1 to other 12

2-2 oranges 6

2 to one and 1-1 to other two persons 12

1-1 to four persons 1

Now according to condition 1, If Ankur receives 1 orange then it is necessary to give

1-1 orange to all others,

Therefore out of 10 methods in which Ankur receives 1 orange only that 1 is correct

in which all

boys get 1-1 oranges.

According to condition 2, Parag has disagreed to receive 3 oranges,

Therefore out of 3 methods in

which Parag gets 3 oranges, 2 are rejected. (One method has been rejected in the

previous condition)

According to condition 3, If Parag obtains 2 oranges then Ankur does not receive any orange,

Therefore out of 6 methods in which Parag receives 2 oranges only 3 are correct.

In remaining 3 methods

2 are rejected in first condition hence 1 method is rejected in this step.

According to condition 4, If Milan gets 3 oranges then Deepak gets 1 orange necessarily

Therefore out of 3 methods in which Milan gets 3 oranges only 1 method is correct.

Out of other 2 methods 1 is rejected. (Other 1 has been rejected in first condition)

According to condition 5, Only Deepak can take all the 4 oranges.

Therefore out of 4 methods

as given in the table above, 3 are rejected

Total no. of rejected methods is 9+2+1+1+3=16

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