CBSE Class 11-science Answered
To solve this question, you have to consider some cases.
case I : let x4=0
x1+x2+x3=20.
You have to distribute 20 identical objects into 3 groups. No. of solutions to this = (20+3-1)C(3-1)=22C2
case II : let x4=1
x1+x2+x3=16
You have to distribute 16 identical objects into 3 groups. No. of solutions to this = (16+3-1)C(3-1)=18C2
case III : let x4=2
x1+x2+x3=12
You have to distribute 12 identical objects into 3 groups. No. of solutions to this = (12+3-1)C(3-1)=14C2
case IV : let x4=3
x1+x2+x3=8
You have to distribute 8 identical objects into 3 groups. No. of solutions to this = (8+3-1)C(3-1)=10C2
case V : let x4=4
x1+x2+x3=4
You have to distribute 4 identical objects into 3 groups. No. of solutions to this = (4+3-1)C(3-1)=6C2
case VI : let x4=5
x1+x2+x3=0
You have to distribute 0 identical objects into 3 groups. No. of solutions to this = 2C2 = 1
Hence total number of solutions = 1 +6C2 + 10C2 + 14C2 + 18C2 + 22C2
= 536