How many ways 10 identical chocolates can be distributed to three people?
How many ways 10 identical chocolates can be distributed to three people?
The correct option is D
Let the number of chocolates person be A, B and C get,
A + B + C = 10
10 chocolates are to be distributed to 3 persons.
To distribute the 10 chocolates to 3 persons, we can do it by making 2 partitions so that 3 groups are formed as shown.
For example, by the above partition, we mean 1st person gets 2 chocolates, 2nd person gets 4 chocolates and 3rd person gets 4 chocolates.
Similarly, other partitions are also possible.
So, distribution of 10 chocolates, essentially means to select the places for 2 partitions (each look like I), in a group of 10 chocolates and 2 I's
In other words, we have to select places for 2 I's out of 12 places.
This can be done is 10+3−1C3−1= 12C2 ways.
Let the number of chocolates person be A, B and C get,
A + B + C = 10
10 chocolates are to be distributed to 3 persons.
To distribute the 10 chocolates to 3 persons, we can do it by making 2 partitions so that 3 groups are formed as shown.
For example, by the above partition, we mean 1st person gets 2 chocolates, 2nd person gets 4 chocolates and 3rd person gets 4 chocolates.
Similarly, other partitions are also possible.
So, distribution of 10 chocolates, essentially means to select the places for 2 partitions (each look like I), in a group of 10 chocolates and 2 I's
In other words, we have to select places for 2 I's out of 12 places.
This can be done is 10+3−1C3−1= 12C2 ways.
