IIT JEE , AIEEE Forum - Mathematics , Algebra

jw

find the number of ways in which 11 indentical apples can be distributed among 6 children so that each child receives atleast one apple.

ans: 252

2) how many + ve integrel soln are there for eqn x+y+z+w = 20

ans: 19 c3

Conjurer

Both are questions based on same concept, the finding the coefficient concept( rather generating functions).

1)For +ve integral solutions , consider the equation

(x + x^2 + x^3.....x^11)(x + x^2 + x^3.....x^11)(x + x^2 + x^3.....x^11)...6 times = 11

Find the coefficient of x^11 in this expansion. :D

sboosy

atri.shivam

1]
each child has to recieve one apple
remaining apples=5
now 5 apples have to be distributed among 6 children where each may recieve 0-6 apples.
c+r-1Cr-1=5+6-1C5-1
=>10C5
=252

2]
to find integral positive sol of x+y+z+w=20
give 1 to x,y,z,w
thus we have to find no of non negative sol of x+y+z+w=16
=>n+r-1Cr-1=16+4-1C4-1
=19C3

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