Q:
      
      
         
            
A Committee of 5 persons is to be formed from a group of 6 gentlemen and 4 ladies. In how many ways can this be done if the committee is to be included atleast one lady?
         
       
      
      
      
          
      
      
          Answer & Explanation
         Answer: C) 246         
         
Explanation: A Committee of 5 persons is to be formed from 6 gentlemen and 4 ladies by taking. 
 
(i) 1 lady out of 4 and 4 gentlemen out of 6 
(ii) 2 ladies out of 4 and 3 gentlemen out of 6 
(iii) 3 ladies out of 4 and 2 gentlemen out of 6 
(iv) 4 ladies out of 4 and 1 gentlemen out of 6 
 
In case I the number of ways =  = 4 x 15 = 60 
In case II the number of ways =  = 6 x 20 = 120 
In case III the number of ways =  = 4 x 15 = 60
In case IV the number of ways =  = 1 x 6 = 6 
 
Hence, the required number of ways = 60 + 120 + 60 + 6 = 246
       
      
      
      
          View Answer
          Report Error
          Discuss