Question
In how many ways can 6 prizes be distributed equally among 3 persons?
- 6C2 × 4C2
- 6P2 × 4P2
- 3
- 36
Hint:
The prizes can be distributed in only one pattern. In this, it can be 2 prizes to each person . So, we will find the number of ways for each of these patterns and hence find the number of ways of distributing the prizes.
The correct answer is: 6C2 × 4C2
Detailed Solution
There are 6 prizes to be distributed equally among 3 persons i.e. 2 prize per person.
For the first person we have to select 2 from 6 = 
For the second person we have to select 2 from 4 = 
For the third person we have to select 2 from 2 = 
Thus, 6 prizes can be distributed equally among 3 persons in 
ways.
In combinatorics, the rule of sum or addition principle states that it is the idea that if the complete A ways of doing something and B ways of doing something and B ways of doing something, we cannot do at the same time, then there are (A + B) ways of choosing one of the actions. In this question, there is a possibility that the student might miss considering all the cases. They may forget to consider case 2 and get a different answer.
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