Question

# In how many ways can 6 prizes be distributed equally among 3 persons?

^{6}C_{2} × ^{4}C_{2}
^{6}P_{2} × ^{4}P_{2}
- 3
- 3
^{6}

^{6}C_{2}×^{4}C_{2}^{6}P_{2}×^{4}P_{2}^{6}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: ^{6}C_{2} × ^{4}C_{2}

### 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 $6 =$

$2=$

For the third person we have to select $2$ from 2$=$

$ways.$

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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