Find the number of permutations and combinations if n = 12 and r = 2.

Explanation

Let `A={a_(1),a_(2),a_(3), . ..,a_(n)}`
For each `a_(i)(1leilen),` we have either `a in P_(j)` or `a_(i) cancel(in)P_(j)(1 le j le m)`. i.e., there are `2^(m)` choices in which `a_(i)(1leilen)` may belong to the `P_(j)`'s.
Out of these, there is only one choice, in which `a_(i) in P_(j)` for all `j=1,2, . .. ,m` which is not favourable for
`P_(1)capP_(2)capP_(3)cap . ..capP_(m)` to be `phi` thus,
`a_(i) cancel(in)P_(1)capP_(2)cap . ..capP_(m)` in `(2^(m)-1)` ways. since, there are n elements in the set A, the total number of choices is `(2^(m)-1)`.