please guide me about the formula

Dear Satyam,

to solve this question, you have to consider some cases.

case I : let d=0

a+b+c=24.

You have to distribute 24 identical objects into 3 groups.no of solutions to this = (24+3-1)C(3-1)=26C2

case II : let d=1

a+b+c = 20

You have to distribute 20 identical objects into 3 groups.no of solutions to this = (20+3-1)C(3-1)=22C2

case III : let d=2

a+b+c=16

You have to distribute 16 identical objects into 3 groups.no of solutions to this = (16+3-1)C(3-1)=18C2

case IV : let d=3

a+b+c=12

You have to distribute 12 identical objects into 3 groups.no of solutions to this = (12+3-1)C(3-1)=14C2

case V : let d=4

a+b+c=8

You have to distribute 8 identical objects into 3 groups.no of solutions to this = (8+3-1)C(3-1)=10C2

case VI : let d=5

a+b+c=4

You have to distribute 4 identical objects into 3 groups.no of solutions to this = (4+3-1)C(3-1)=6C2

case VII : let d=6

a+b+c=0

You have to distribute 0 identical objects into 3 groups.no of solutions to this = 2C2

Hence total number of solutions = 1 +6C2 + 10C2 + 14C2 + 18C2 + 22C2 + 26C2

                                                    = 861

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