in how many ways can we distribute 10 identical looking pencils to 4 students so that each student gets at least 1 pencil?

• first we distribute 4 pencils each 1 to 4 students. remaining pencils are 6. then ways of distributions are (n+r-1)C(r-1) here n=6 & r=4
  hence 9C3=84
• 12 years agoHelpfull: Yes(146) No(12)
• first we shall distribute 4 pencils to each student.now we have 6 pencils remaining.using stars and bars formula we get(6+4-1)c(4-1)=9c3=84
• 11 years agoHelpfull: Yes(36) No(0)
• please explain properly.
  how we got n+r+1 c r-1
• 11 years agoHelpfull: Yes(14) No(8)
• ANS:210
  out of 10 4 is distributed to students, so 6 is remaining
  now, we will distribute remaining 6 pencils to 10 students in 10C6 ways
  =10C4= (10*9*8*7)/(4*3*2*1)=210
• 12 years agoHelpfull: Yes(9) No(153)
• To get each student gets at least 1 pencil.First, we distribute 4 pencils each 1 to 4 students.
  Remaining pencils are 6(Total 10 pencils we already distribute 4 pencils).
  Number of ways of distributing n identical things among r persons when each person may get any
  number of things =(n+r-1)C(r-1)
  here n=6 & r=4
  hence 9C3=84
  Therefore answer is 84 ways.
• 7 years agoHelpfull: Yes(6) No(0)
• Since the pencils are identical, we can just give one to each student leaving six to be given out. The number of ways to distribute n identical objects among r people is given by (n+r−1)c(r−1). For our problem, this is (93)=84.
• 9 years agoHelpfull: Yes(3) No(1)
• posibility of 10 pencils to 4 persons is 10c4 is 210
• 10 years agoHelpfull: Yes(0) No(20)
• 1st each needs 1
  So 10C4 = 210
  2nd 6 to 4 students including 0
  What is the number of ways in which n identical objects can be divided into r groups where each group can have any number of objects including 0?
  The formula is (n+r-1) C (r-1)
  This is called the Bose-Einstein coefficient
  
  (6+4-1)c(4-1)=9c3=84
  210 x 84 =17640
  
• 9 years agoHelpfull: Yes(0) No(13)