Flag Algebra> P c question...
question mark

Q.13 Find the number of ways in which the number 3 0 can be partitioned into three unequal parts, each
part being a natural number. What this number would be if equal parts are also included.

Ans : 61 , 75

APURV GOEL , 13 Years ago
Grade 10
anser 3 Answers
kushal satya

Last Activity: 13 Years ago

LET THE THREE NOS BE x,y,z such that x>y>z

let x-y=k where k>0

y-z=j j>0

this implies that

x+y+z=3z+2j+k where z<28

no of solutions=coefficient of x30 in (x+x2+..........x27)3(x+x2=......)2(x+x2=......)

=coefficient of x30 in x6(1-x)-6

=coefficient of x24 in (1-x)-6

=24C5

kushal satya

Last Activity: 13 Years ago

in the above solution coefficient of x6 would be 29C5.

kushal satya

Last Activity: 13 Years ago

APURV PLEASE IGNORE THE ABOVE SOLUTION. IT WAS WRONG.

THE CORRECT SOLUTION IS AS FOLLOWS.

ET THE THREE NOS BE x,y,z such that x>y>z

let x-y=k where k>0

y-z=j j>0

this implies that

x+y+z=3z+2j+k where z<28

no of solutions=coefficient of x30 in (x3+x6+..........x27)(x2+x4......)(x+x2 +......)

=coefficient of x30 in x6(1-x3)-1(1-x2)-1(1-x)-1

=61

star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments