apti combinatroy

Question

Q) a person has to divide his assesta worth rs 30 crore in 3 parts to be given to three of his sons ajay ,ram ,sham ensuring that every son gets assests atleast worth rs 5 crore . in how many ways can this be done if it is given that three sons should get their share in multiple of rs 1 crore ?

can this be done with ordered partition ???

Answer 1

Total money = 30 Cr 

Each son must get 5+x, 5+y, 5+z

wkt 5+x+ 5+y+ 5+z = 30

i,e; x+y+z=15 

Now we can find Non-Intergral solution for this =^(n+r-1)C_r-1

where n=15 and r=3

^(n+r-1)C_r-1 = 17C₂

Therefor totally 17C₂ ways are there.

Comments

please explain me the formula you have used here n+r-1Cr-1

what i know is that r nondistinct objects into n distinct cells where a cell can hold more than one object
C(n+r-1,r)

kindly help me

---

Watch this video you will get it

https://www.youtube.com/watch?v=7DxqCgC0oLo&index=6&list=PLsFENPUZBqioyqffh3YZ2pKUg4uZFQJUY