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?

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+3-1C_3-1 =⁷C₂

integral solution of equation 2nd

^4+3-1C_3-1 =⁶C₂

integral solution of equation 3rd

^3+3-1C_3-1 =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

---

Please feel free to post as many doubts on our discussion forum as you can.
 If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly.
 We are all IITians and here to help you in your IIT JEE  & AIEEE preparation.

 All the best.
 
Regards,
Askiitians Experts
Badiuddin