The following question involves a standard deck of 52 playing cards. In such a deck of cards there are four suits of 13 cards each. The four suits are: hearts, diamonds, clubs, and spades. The 26 cards included in hearts and diamonds are red. The 26 cards included in clubs and spades are black. The 13 cards in each suit are: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. This means there are four Aces, four Kings, four Queens, four 10s, etc., down to four 2s in each deck. You draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second. (a) Are the outcomes on the two cards independent? Why? Yes. The probability of drawing a specific second card is the same regardless of the identity of the first drawn card. Yes. The events can occur together. No. The probability of drawing a specific second card depends on the identity of the first card. No. The events cannot occur together. (b) Find P(ace on 1st card and nine on 2nd). (Enter your answer as a fraction.) (c) Find P(nine on 1st card and ace on 2nd). (Enter your answer as a fraction.) (d) Find the probability of drawing an ace and a nine in either order. (Enter your answer as a fraction.)

Q: Assume that you have a 52-card deck at hand and you are planning to draw 6 cards from the deck. How…

A: We have,Number of cards in deck = 52Number of cards are planning to draw from deck = 6

Q: If there are 57 cards in a deck and 12 are dealt to each student, how many 12 card possibilities are…

A: Combination Rule:The arrangement of r objects from n different objects is given by:

Q: There are 52 cards in a standard deck. Thirteen of those cards are spades. The deck is shuffled and…

A: Given that there are 13 spades.  We have to select 3 spades from the 13 spades.    Since the order…

Q: Joe has 6 favorite baseball teams, and he put their flags on his flagpole in random order. How many…

A:

Q: From a standard deck of cards, how many 10 card hands can be dealt that contain exactly 3 aces?

A: We have given information,  In a standard deck of cards, 10 card hands can be dealt.

Q: A box contains 8 red balls, 8 blue balls, and 6 orange balls. In how many ways can 6 balls be chosen…

A: Given : A box contains 8 red balls, 8 blue balls, and 6 orange balls

Q: A group of 10 people is choosing a chairperson and vise-chairperson. They put all 19 people's name…

A: Note: given that there are total of 10 people. Thus there is only chance to put 10 peoples name into…

Q: deck of cards has 2 black, 5 green, and 6 blue cards. You pick 2 cards from the deck. Cards are…

A:

Q: From a standard​ 52-card deck, how many 7​-card hands consist of 5 clubs and 2 diamonds​?

A: There are total 13 clubs and 13 diamonds.  We can pick 5 clubs from 13 clubs in 13C5 ways. We can…

Q: A group of 8 people, A, B, C, D, E, F, G, and H are visiting an amusement park. More drama. A and B…

A:

Q: In a poker game, a player is dealt a 9 card "hand" from a deck of 52 distinct cards. How many…

A: Total number of distinct cards are 52 Number of cards to be chosen are 9 Given the cards are…

Q: Your car seats 5 people, including the driver. You have 4 friends who all do not have driver’s…

A: The objective of this question is to find out the number of different ways the 4 friends can arrange…

Q: If a 8 card hand is dealt from an ordinary 52 card deck, in how many of those hands are all 8 cards…

A:

Q: The card game Cribbage uses a standard 52 card deck. Each player is dealt 4 cards, and the order…

A: The number of combinations of 4 card from the set of 52 cards is, n=C452=52×51×50×494×3×2×1=270725

Q: 10 people is choosing a chairperson and vice chairperson

A: Given that   A group of 10 people = (n)=10 We have to select two people from total 10 people.…

Q: How many different 4 card hands can be dealt from a deck of 52 cards? Your answer is :

A:

Q: You are playing a game with a standard 52 card deck. In this game each player gets 3 cards, and the…

A: We can use combinations to find the answer. There are 52 cards and each player gets 3 cards.

Q: The card game Cribbage uses a standard 52 card deck. Each player is dealt 4 cards, and the order…

A: Given that, The card game Cribbage uses a standard 52 card deck. Each player is dealt 4 cards Order…

Q: The following question involves a standard deck of 52 playing cards. In such a deck of cards there…

A: As per our policy we are allowed to solve three sub parts at a time since, you have uploaded…

Q: our cards are dealt from a standard deck of 52 cards. How many ways can you be dealt three aces and…

A: Four cards are dealt from a standard deck of 52 cards. There are 4 cards of aces in the deck. There…

Q: Suppose you choose 9 cards from a standard 52-card deck (with 13 hearts, 13 spades, 13 clubs and 13…

A: A standard 52-card deck contains 13 hearts, 13 spades, 13 clubs and 13 diamonds and probability of…

Q: From a standard​ 52-card deck, how many 6​-card hands consist entirely of face​ cards?

A: The standard deck of cards contains total 52 cards.

Q: How many 13-card bridge hands can be chosen from a deck of cards

A: Ans:-  How many 13-card bridge hands can be chosen from a deck of cards?

Q: A bride is choosing a dress for her bridesmaids. If there are 3 styles, 5 colors, and 4 fabrics, in…

A: Given: Styles = 3 Colors = 5 Fabrics = 4 The number of ways that she can select the bridesmaids…

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.