In how many ways can 20 identical pencils be distributed among three girls so
that each gets at least 1 pencil?

• 
  
  consider 3 girls as A,B,C THEN A+B+C=20, but each one should get atleast 1 pencil so giving 1 pencil to each student,
  the remaining pencils are 20-3=17
  now A'+B'+C''=17,
  number of non negative integers of A',B',C' are (17+3-1)C(3-1)
  
  so total Combinations are 19c2=19*9 = 171,
• 12 years agoHelpfull: Yes(24) No(3)
• simple formula for this kind of problems is
  
  (n-1)c(r-1)
  
  so 19c2= 171
  
• 12 years agoHelpfull: Yes(24) No(1)
• Garima Nice answer Can u please explain solution for previous question??
• 12 years agoHelpfull: Yes(3) No(5)
• 171 is Correct answer. 19C2=171
• 12 years agoHelpfull: Yes(1) No(4)
• GARIMA CAN U PLS EXPLAIN ME THE LOGIC BEHIND (17+3-1)C(3-1) CALCULATION
• 12 years agoHelpfull: Yes(1) No(1)
• plz explain it.....
• 12 years agoHelpfull: Yes(1) No(1)
• what if each girl gets at least 2 pencils then what would have been the solution considering your formula (n-1)C(r-1)
• 12 years agoHelpfull: Yes(1) No(0)
• The first girl can take from 1 to 18 pencils. If she takes 1, the second girl can take
  from 1 to 18. If she takes 2, the second girl can take from 1 to 17, and so on. The
  third girl simply takes whatever is left. Hence the total number of ways is
  18+17+…+1=(18*19)/2 =171.
• 12 years agoHelpfull: Yes(1) No(0)