In the card game Red 7, the deck consists of 49 cards, with cards numbered 1 through 7 in each of the seven colors of the rainbow (red, orange, yellow, green, blue, indigo, violet). All 49 cards are distinct. You are dealt a hand of seven cards. Answer each question and briefly explain your reasoning. Leave your answer unsimplified in terms of permutations, combinations, exponents, etc. (a) How many seven-card hands are possible? (b) How many seven-card hands contain no blue cards? (c) How many seven-card hands contain all cards of the same color? (d) How many seven-card hands contain one card of each color? (e) How many seven-card hands contain at least one red card