Determine the number of ways to distribute 10 (indistinguishable) orange drinks, 1 lemon drink, and 1 lime drink to four thirsty students such so that each student gets at least one drink, and the lemon and lime drinks go to different students.

• first we have give 1 lemon and 1 lime drink to 2 distinct persons.
  For this 1st we have select 2 out of 4 persons in 4c2 ways and arrange in 2! ways
  Then for satisfying the condition of atleast one, give 2 orange drinks of rem 2 people in 1 way(since identical).
  now we have 8 orange drinks to be distributed it to 4 drinks.
  for this we can use the formula (n+r-1)c(r-1) where n=8 and r=4
  Hence the final ans is (8+4-1)c(4-1)*4c2*2!=1980.
• 11 years agoHelpfull: Yes(18) No(0)
• 4 choices for who gets the lemon drink.
  3 choices for who gets the lime drink.
  Then give an orange drink to each of the other two, leaving 8 orange drinks.
  
  Now you have satisfied all the conditions, except for distributing all the drinks.
  
  Now put the 8 orange drinks in a row: o o o o o o o o
  We will put divide them up into 4 groups by putting | markers in 3 places.
  For example:
  o o | o | o o o o | o would mean first kid gets 2, next gets 1, next gets 4, next gets 1.
  or
  o o o o o o o o | | | means first kid gets all 8.
  
  So we have 8 circles and 3 bars to arrange.
  We can view that as 11 positions and we choose any 3 for the bars.
  That is, there are 11 C 3 ways to do it.
  
  So the answer is 12 (the number of ways of doing the first 4 drinks) * 11 C 3,
  which is 12 * 165 = 1980
• 11 years agoHelpfull: Yes(15) No(6)
• Sorry, the answer is 4P2*9C3
• 11 years agoHelpfull: Yes(8) No(4)
• my previous answer was wrong.....it should be 4c2 * 11c3 = 990
• 11 years agoHelpfull: Yes(2) No(4)
• 2 distinct drinks that are lemon and lime can be given to 4 students in 4P2 ways and 10 identical orange juice can be given to 4 students such that each gets atleast 1 is 10C3. So the final solution is 4P2*10C3
• 11 years agoHelpfull: Yes(1) No(2)
• @GAURAV JAISWAL heyy gaurav what is the real answer????
• 11 years agoHelpfull: Yes(1) No(1)
• http://answers.yahoo.com/question/index?qid=20100207182917AAlCeLV get the correct ans here
• 11 years agoHelpfull: Yes(1) No(1)
• 4c2*2x10c4
• 11 years agoHelpfull: Yes(0) No(0)
• 4C2 * 10 * 9 * 8 * 7 = 30240
• 11 years agoHelpfull: Yes(0) No(0)
• 4c2=12 ese
• 11 years agoHelpfull: Yes(0) No(2)
• 10c3×2!
  its formula to ditribute n things to k people n-1ck-1 so first consider 1lime and 1 lemon can be given to one studen den multiply it with 2!
• 11 years agoHelpfull: Yes(0) No(3)
• 4p2 x 11c3
• 11 years agoHelpfull: Yes(0) No(0)