Maths-
General
Easy

Question

The number of ways in which 20 volunteers can be divided into groups of 4, 7 and 9 persons is-

  1. 16C7× 13C2    
  2. 20C7 × 11C4    
  3. 20C4 × 16C7    
  4. 20C9 × 13C9    

hintHint:

Since  we have to make groups of 4, 7 , 9 people out of 20 volunteers , find out the number of people that can be selected and similarly those who are selected in one group , they will not participate in other groups.

The correct answer is: 20C4 × 16C7


    We have to make groups of 4, 7 , 9 people out of 20 volunteers
    4 people out of 20 can be selected in C presuperscript 20 subscript 4 space w a y s.
    7 people out of remaining 16 can be selected in C presuperscript 16 subscript 7 space w a y s.
    9 people out of remaining 9 can be selected in C presuperscript 9 subscript 9 space w a y s space equals space 1.

    Thus, the number of ways in which 20 volunteers can be divided into groups of 4, 7 and 9 persons is
    C presuperscript 20 subscript 4 space cross times C presuperscript 16 subscript 7 space.

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