Let A = {1, 2, 3, 4, 5, 6, 7). a. How many subsets of A are there? That is, find [P(A)|. b. How many subsets of A contain exactly 6 elements? c. How many subsets of A contain only even numbers? A standard deck of cards consists of four suits (clubs, diamonds, hearts, and spades), with each suit containing 13 cards (ace, two through ten, jack, queen, and king) for a total of 52 cards in all. How many 7-card hands will consist of exactly 2 hearts and 3 clubs? How many 15-bit strings (that is, bit strings of length 15) are there which: a. Start with the sub-string 011? b. Have weight 6 (i.e., contain exactly 6 1's) and start with the sub-string 011? ED