S={1,2,3,4,5,6,9} 3 n Type numbers 3,6,9 3n−1 Type numbers 2,5 3n−2 Type numbers 1,4 Let NP= Number of Subset of S containing p element which are not divisible by 3 . For P=1 2C1+2C1=4
For P=2 3C12C1+3C12C1+2C2+2C2=14 For P=3 3C1(2C2+2C2)+3C2(2C1+2C1)+2C22C1 +2C12C2=22 For P=4 3C1[2C22C1+2C12C2]+3C2(2C2+2C2) +3C3(2C1+2C1)=22 For P=5 3C2(2C22C1+2C12C2)+3C3(2C2+2C2)=14 For P=6 3C3(2C22C1+2C12C2)=4