(1) S is a set consisting of all alphabets available in English language. The number of elements of S is 26. A subset set C of S is defined as C= fe, f, g, h, i, j}. Consider all possible words that can be built out of 26 alphabets ( from S) having word length exactly equal-to seven. (i) Count the number of words containing atleast one letter from C. 2 (ii)Count the number of words having exactly three letters from the set C. (2) A new programming language for machine learning is being designed by a Data Science company. It was decided that all variable names should be constructed using letters from the set B = {a, b}. For example aa,abb, aabb etc are some valid variable names. The design team wants to know how many variable names of a given length n have three consecutive entries of alphabet 'a'. (a) Is it possible to construct a recurrence relation to count the number of variable names that have three consecutive entries of alphabet 'a' If yes derive it along with the initial conditions. If no give reason. (b) How many variable names of length six have the above property