Discrete math PROJECT 3-COUNTING SUBSETS (BINOMIAL COEFFICIENTS) Choose 6 letters of the English alphabet including all the different characters in your family name. (If you have more than 6 different characters, choose the first 6). Let X be the set of all lower case versions of the letters you have chosen. ) Using correct set notation, ist the elements in set X Gi) List all the subsets of X with 1 letter. How many such subsets are there? Describe how you obtained your list and provide a formula that also gives the number of subsets with 1 letter. (i) Describe how you might find all subsets of X with 2 letters. Do NOT list them. Use an appropriate formula to calculate how many subsets there (iv) Repeat the calculation of part (ii) to find the number of subsets of U of size 0, 3, 4,5 and 6 respectively. (v) Cakculate the sum of your answers. From your lecture notes, what is the value of P() (vi) Based on your calculations above, make an hypothesis about the sum of the binomial coefficients in the expansion of (y)