Maths-
General
Easy

Question

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

  1. 6C2 × 4C2    
  2. 6P2 × 4P2    
  3. 3    
  4. 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 = C presuperscript 6 subscript 2
    For the second person we have to select 2 from 4 = C presuperscript 4 subscript 2
    For the third person we have to select 2 from 2 = C presuperscript 2 subscript 2 space equals space 1
    Thus, 6 prizes can be distributed equally among 3 persons in C presuperscript 6 subscript 2 cross times C presuperscript 4 subscript 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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