Permutations and Combinations Part 1

S = {1, 2, 3, 4, 5, 6, 9}
3n 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
For P = 4
For P = 5
‌3C2(‌2C2‌2C1+‌2C1‌2C2)+‌3C3(‌2C2+‌2C2)=14
For P = 6
‌3C3(‌2C2‌2C1+‌2C1‌2C2)=4
Total Subsets =4+14+22+22+14+4=80