In how many ways can a deck of cards be distributed to 5 players if each player will receive 4 cards

In a doctor’s waiting room, around the dining table on a Saturday night, or in the tent on a rainy camping trip—anytime is the perfect time for playing cards with your Brisbane Kids! If it’s been a while since you’ve shuffled and dealt a deck of cards, here’s a reminder of the rules for six easy card games that will keep your Brisbane Kids amused for hours. Best of all, all six games can be played with one standard deck of cards. Keep a pack in your car glove box, your hand bag and your house so you’ll always have an answer to, “I’m bored”!

1. Go Fish/Fish

Object of the game: To collect as many sets of four as possible.

Players: Two to six players, ages four and up.

The deck: A standard 52 card deck or a tailor made junior version.

Gameplay: Five cards are dealt to each player if three to six players are involved. With only two players, seven cards are dealt to each. All remaining cards are placed face down in a draw pile. Randomly choose a player to go first.

On your turn, ask a player for a specific card rank. You must already hold at least one card of the requested rank. If the player you ask has any cards of the requested rank, she must give all of her cards of that rank to you.

If you get one or more cards from the player you ask, you get another turn. You may ask any player for any rank you already hold, including the same one you just asked for.

If the person you ask has no relevant cards, they say, “Go fish.” You then draw the top card from the draw pile.

If you happen to draw a card of the rank asked for, show it to the other players and you get another turn. However, if you draw a card that’s not the rank you asked for, it becomes the next player’s turn. You keep the drawn card, whatever rank it is. The next player is the one who said “Go fish.”

When you collect a set of four cards of the same rank, immediately show the set to the other players and place the four cards face down in front of yourself.

Go Fish continues until either someone has no cards left in their hand or the draw pile runs out. The winner is the player who then has the most sets of four.

2. Old Maid

Object of the game: To avoid being the player who ends the game holding the Old Maid.

Players: Two to eight players, ages four and up.

The deck: A standard 52-card deck. Remove three of the queens from the deck. The remaining queen is the Old Maid. Alternatively, you can use a tailor made junior version.

Gameplay: Deal the cards as evenly as possible among the group. It’s acceptable for some players to have more cards than other players.

Players sort their cards and discard any pairs. (If a player has three of a kind, he discards two of the cards and keeps the third). The dealer then offers his hand, face down, to the player on his left. That player randomly takes one card from the dealer. If the card matches one he already has in his hand, he puts the pair down. If not, he keeps it.

Play proceeds clockwise, so the player to the left of the dealer then offers his hand, face down, to the player on his left. This cycle repeats until there are no more pairs and the only remaining card is the Old Maid.

The game ends when the Old Maid is the only card in play. The person holding the Old Maid loses.

3. Concentration/Memory

Object of the game: To collect the most pairs of cards.

Players: One to six players, ages three and up.

The deck: A standard 52-card deck. Shuffle the cards and lay them on the table, face down, in a pattern (e.g. 4 cards x 13 cards).

Gameplay: The youngest player goes first. Play then proceeds clockwise.

On each turn, a player turns over two cards (one at a time) and keeps them if they match numbers. If they successfully match a pair of numbers, that player also gets to take another turn.

When a player turns over two cards that do not match numbers, those cards are turned face down again and it becomes the next player’s turn.

To make the game easier, cards can be removed in sets of four (e.g. all of the 2’s and 3’s).

When all the pairs have been found, the player with the most pairs wins.

4. Snap

Object of the game: To win all of the cards.

Players: Two to 12 players, ages three and up.

The deck: A standard 52-card deck or a junior deck of custom Snap cards. The dealer shuffles the cards and deals them as evenly as possible to all of the players. It’s fine for some players to have one card more than other players. Each player places his cards, face down, in a pile in front of him.

Gameplay: The player to the left of the dealer goes first. Play then moves clockwise.

On his turn, each player turns over the top card from his face-down pile. When someone turns over a card that matches a card already face up on another player’s pile, players race to be the first to call “Snap!”. The player who calls “Snap!” first wins both piles and adds them to the bottom of his face-down pile.

When a player calls “Snap!” at the wrong time, he must give his top card to the player who just played. If a player makes a mistake on his own turn, he must give his top card to the player on his right.

Play continues until one player wins all of the cards. That player wins the game.

5. Scumbags and Warlords/Rascals and Royalty

Object of the game: To be the first person in a round of play to get rid of all their cards, and become the “royalty”. If unsuccessful, each player tries to avoid being the last person holding cards, known as the “rascal”.

Players: This game requires a minimum of three players, but may have up to eight players, and is best suited to children aged eight years and older.

The deck: You will need a standard 52 card deck. There are a number of variations but the standard ranking of cards has 2 as the highest card, followed by the Ace, King, Queen, and Jack, and then 10-3.

Game Play: Deal out all the cards, even if the distribution is not equal. The player to the dealer’s left goes first and lays face up a card or set of cards of the same rank. The next player may either pass or make a play that exceeds that ranking. To exceed the previous cards, the player must play the same number of cards and they must rank higher. For example, a player plays two tens.

The next player may play two Jacks, but may not play three nines, since these are lower in rank, nor can she play three Kings. She may also play two Kings. If the player has no suitable cards to play, they can opt to pass.

Play continues until three consecutive players are unable to beat the previous cards played, at which point the cards on the table are removed from the game for that round and the last person to play may lead out a new card or cards.

The first player to run out of cards will be the “royalty” on the next round, but play continues until all but one player is left with cards. Whoever ends up with cards in their hands once everyone else is out of cards is declared the “rascal” and must deal the next hand.

6. Spoons/Donkey

Object of the game: To be the first to collect four cards of the same rank. If an opponent beats you to that goal, the aim is to not be the last to realise it (or you will be declared the “donkey”).

Players: This game can be played with three to 13 players and will best suit children aged eight years and older.

The deck: A standard 52-card deck. For each player in the game, you need four cards of the same rank from the deck. For example, with five players you could use the Aces, 2s, 3s, 4s and 5s. You will also need one spoon for each player, minus one. For example, with eight players, you will need seven spoons. For a fun and tasty alternative, use chocolates instead of spoons!

Game play: Shuffle the cards and deal them to the players. Each player will have four cards. Put the spoons in the middle of the table so that every player can reach them.

Players simultaneously choose one card from their hands, pass that card to the opponent on their left, and pick up the card they’ve received from the opponent on their right. Each player can never have more than four cards in their hand.

When a player collects four of a kind, they take a spoon, as subtly as possible, and place it in front of themselves.

When one player does this, every other player must do likewise as quickly as possible. The last player to grab a spoon is eliminated from the game. Remove a set of four cards from the deck and play another round. The final two players in the game are co-winners.

For some more wet weather inspiration, check out our collection of the Best Rainy Day Ideas in Brisbane for Kids. If card games are a bit tricky for your little one, you may like our list of Board Game Ideas for Toddlers.

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Answer

Hint: A) For the first part, firstly, we will choose the suit to distribute to each player and then calculate the number of ways to distribute them. Then we will distribute remaining cards to all of them.B) For the second part, we will choose ace, king, queen and jack to distribute to each player. Then we will distribute remaining cards to all of them.

Complete step-by-step answer:

Note: We used permutations to solve above questions. Note that in both cases, the number of ways to distribute the remaining $48$ card to $4$ groups is $ = \dfrac{{48!}}{{12! \times 12! \times 12! \times 12!}}$ . We divided by $12! \times 12! \times 12! \times 12!$ because we have to arrange them in groups. If we were arranging $48$ cards to $48$ groups then we would have divided by $1! \times 1! \times 1! \times 1!$ which is eventually $48!$.