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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?

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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