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1) In how many ways we can give 5 apples ,4mangoes and 3 oranges to three persons if each may recieve none,one or more? 2)A number lock has 4 dials each dial has the digits 0,1,2,.................,9.What is the maximum unsuccessful attempts to open the lock?

1) In how many ways we can give 5 apples ,4mangoes and 3 oranges to three persons if each may recieve none,one or more?


2)A number lock has 4 dials each dial has the digits 0,1,2,.................,9.What is the maximum unsuccessful attempts to open the lock?

Grade:Upto college level

1 Answers

Badiuddin askIITians.ismu Expert
147 Points
11 years ago

Dear Vanya

let 1st person get x1 appple ,x2 mangoes , x3 oranges

2nd  person get y1 appple ,y2 mangoes , y3 oranges

3rd person get z1 appple ,z2 mangoes , z3 oranges

so x1 +y1+ z1=5 ...........1

  x2 +y2 +z2 =4...............2

 x3+y3+z3 =3................3

where x1,x2,x3,y1,y2,y3.z1.z2.z3 ≥ 0

integral solution of equation 1st

5+3-1C3-1 =7C2

integral solution of equation 2nd

4+3-1C3-1 =6C2

integral solution of equation 3rd

3+3-1C3-1 =5C2

so total ways =7C26C25C2

 

2 question

each dial has 10 possibility

so total possibility=10*10*10*10

out of this one is succecful attemmpt

so mas unsuccesful attempt=9999


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