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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
10 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
10 years ago

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

kushal satya
37 Points
10 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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