Maths-
General
Easy

Question

Twelve students compete for a race. The number of ways in which first three places can be taken, is-

  1. 12 ! – 3    
  2. fraction numerator 12 factorial over denominator 3 factorial end fraction    
  3. 12 cross times 11 cross times 10    
  4. 3 !    

hintHint:

There are only 3 prizes to be given to any 3 people out of 12. So if 1 person gets first prize, he will not be counted for second prize and so on....

The correct answer is: 12 cross times 11 cross times 10


    The number of ways to select the winner of the first prize is C presuperscript 12 subscript 1     
    The number of ways to select the winner of the second prize is C presuperscript 11 subscript 1 (11, since one student is already given a prize)    
    The number of ways to select the winner of the third prize is C presuperscript 10 subscript 1 (10, since two students are already given a prize)            
     Thus, total number of ways is C presuperscript 12 subscript 1 ×C presuperscript 11 subscript 1× C presuperscript 10 subscript 1 = 12 × 11 × 10 = 1320

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