in how many ways can we distribute 10 identical looking pencil to 4 students so that each student gets at least one pencil?
a)5040
b)210
c)84
d)none of these

• there are 10 pencils
  so 1 given to each
  hence 6 remains
  as per product rule and sum rule
  4*(6+5+4+3+2+1)=84
• 12 years agoHelpfull: Yes(58) No(12)
• In 84 ways can we distribute 10 identical looking pencil to 4 students so that each student gets at least one pencil.
  
  consider 4 students as A,B,C,D THEN A+B+C+D=10, but each one should get atleast 1 pencil so giving 1 pencil to each student,
  the remaining pencils are 10-4=6
  now A'+B'+C'+D'=6,
  number of non negative integers of A',B',C',D' are (6+4-1)C(4-1)
  
  so total Combinations are 9c3=84,
• 12 years agoHelpfull: Yes(36) No(20)
• ans: 84.
  we can divide these pencils as:
  A B C D total permutation under this division
  7 1 1 1 4!/3!=4( divided by 3! becoz 1 is repeted three times)
  6 2 1 1 4!/2!=12
  5 2 2 1 4!/2!=12
  5 3 1 1 4!/2!=12
  4 2 2 2 4!/3!=4
  4 3 2 1 4!=24
  4 4 1 1 4!/(2!*2!)=6
  3 3 3 1 4!/3!=4
  3 3 2 2 4!/(2!*2!)=6
  add all the aboves u will get 84...
• 12 years agoHelpfull: Yes(22) No(5)
• ans-number of ways of distributing n identical things among r person where Each person get atleast one things then formula is (n-1)C(r-1).
• 10 years agoHelpfull: Yes(11) No(1)
• 84 is correct please explain it neatly....
  
• 12 years agoHelpfull: Yes(7) No(5)
• b)210
  10c4=210
• 12 years agoHelpfull: Yes(5) No(46)
• (n-1)C(r-1)=9C3=84
• 10 years agoHelpfull: Yes(5) No(2)
• @vivek..plz explain your rule.I can't undrstnd..:(
  @garima..i think this is right.
• 12 years agoHelpfull: Yes(3) No(3)
• ans a(5040).
  for 1st=10ways
  for 2nd=9ways
  for 3rd=7ways
  for 6th=6ways
  10*9*8*7=5040 answer
• 12 years agoHelpfull: Yes(2) No(45)
• n-1cr-1=10-1c4-1=9c3=84
• 9 years agoHelpfull: Yes(2) No(1)
• give 1 for four students. remaining is 6
  6+4-1c4-1=9c3
  9c3=84
• 8 years agoHelpfull: Yes(1) No(0)
• we have 10 identical pencils,
  Task1: distribute 1 pencil each = 1 way ; remaining 6 pencils
  
  Task2: Distribution of 6 identical objects to 4 distinct students is C(6+4-1 , 6)
  
• 9 years agoHelpfull: Yes(0) No(1)