10 different books and 2 different pen are given to 3 boys so that each get equal no. of things.Probability that same boy doesn't receive both pens is__________ans:8/11

Dear shefali

probability of same boy doesn't receive both pens = 1 - probabilty of any  boy  receive both pens

since all the student recieves same number of article.so each one get (10+2)/3 =4         

number of ways in which 10 books and 2 pen is distributed to 3 student is =¹²C₄ ⁸C₄ ⁴C₄

 now find the number of ways such that any boy recieve the both pen...

select one boy from 3 and give both pen to him in = ³C₁ * 1 ways

 rest two article can be given to this boy in = ¹⁰C₂ ways 

  other 2 boys will get article in ⁸C₄ *⁴C₄ ways

so number of ways such that any boy recieve the both pen= ³C₁ * 1*¹⁰C₂ *⁸C₄ *⁴C₄

so required probability = 1- ³C₁ * 1*¹⁰C₂ *⁸C₄ *⁴C₄ / ¹²C₄ ⁸C₄ ⁴C₄

                                          =8/11

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