A subsequence of a sequence x = hx1, x 2 , . . . , xni is a sequence hxi1 , xi 2 , . . . , xi k i of k ≥ 0 elements of x, where hi 1 , i 2 , . . . , ik i is a strictly increasing sequence. For...

A subsequence of a sequence x = hx1, x₂, . . . , xni is a sequence hxi1 , xi₂
, . . . , xi_k
i of k ≥ 0 elements of x, where hi₁, i₂, . . . , ik i is a strictly increasing sequence. For example, PYTHON is a subsequence of PYTHAGOREAN and BASIC is a subsequence of BRAINSICKNESS.

Suppose the components of x = hx₁, x₂, . . . , xni are all different (as in PYTHON but not PYTHAGOREAN). Use the Mapping Rule to figure out how many subsequences of x there are.