IIT JEE , AIEEE Forum - Mathematics , Algebra

kusum

how many positive integral soutions are there for the equation x+y+z+w=20?

please do using marker method and explain.

AAKRITI

No. of non negative solutions to x+y+z+w=20 is equal to no. of ways of arranging 20 identical balls and (4-1) separators. Therefore total no. of objects= 20 + 3 and no. of permutations= ( 20+3 )!/ (20)!. 3!

deepak_agarwal

i will tell you a general way to solve these types of problems in pnc.....see a ques like x+y+z=20....integral soln???

take z on rhs....so x+y=20-z...take z=0,1,2,.....19...so x+y=20,19,18....1...so solutions of each is 21,20,19.........2...add all of them and get the ans....

another method..which is useful here in this ques....ans to ...x+y+z+....nth time=m is coefficient of x^m in (x+x^2 +x^3+....

)^n...right dude.....

uday_sravan

Finding no. of integral solutions of the equation x+y+z+w=20 is same as dividing & arranging 20 things among 4 groups.

Dividing & arranging 'n' different things among 'r' groups can be done in n+r-1Cr-1 ways.

So here no. of ways are 23C3=1771

deepak_agarwal

right..

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