In a certain children's card game, a player has a deck of 40 cards. Each of...

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In a certain children's card game, a player has a deck of 40 cards. Each of those 40 cards is either a monster card, a spell card, or a trap card (with each card being exactly one of these). This player's 10 card deck has 19 monster cards, 15 spell cards, and 6 trap cards, that may or may not be distinct from one another (there are potentially identical copies of the same card, or not). Each game begins with drawing a 5 card hand from the deck, called "the opening hand". (a) Suppose every card in the player's deck is distinct (so all 40 cards are unique). In how many ways can the player have an opening hand with only spell cards? (b) Suppose every card in the player's deck is distinct (so all 40 cards are unique). In how many ways can the player have an opening hand with 2 monster cards, 2 spell cards, and 1 trap card? (c) Suppose every card in the player's deck is distinct (so all 40 cards are unique). In how many ways can the player have an opening hand with at least 2 monster cards and at least 1 spell card? In a certain children's card game, a player has a deck of 40 cards. Each of those 40 cards is either a monster card, a spell card, or a trap card (with each card being exactly one of these). This player's 10 card deck has 19 monster cards, 15 spell cards, and 6 trap cards, that may or may not be distinct from one another (there are potentially identical copies of the same card, or not). Each game begins with drawing a 5 card hand from the deck, called "the opening hand". (a) Suppose every card in the player's deck is distinct (so all 40 cards are unique). In how many ways can the player have an opening hand with only spell cards? (b) Suppose every card in the player's deck is distinct (so all 40 cards are unique). In how many ways can the player have an opening hand with 2 monster cards, 2 spell cards, and 1 trap card? (c) Suppose every card in the player's deck is distinct (so all 40 cards are unique). In how many ways can the player have an opening hand with at least 2 monster cards and at least 1 spell card?