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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

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

Grade:10

3 Answers

kushal satya
37 Points
9 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
37 Points
9 years ago

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

kushal satya
37 Points
9 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

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