How many different 5-card hands with at least 3 hearts can be dealt from a standard deck of 52 cards?Hint: See “Did You Know?” on page 535 of the textbook if you are not familiar with a standard deck of cards.a.517,644b.211,926c.241,098d.2,543,112

A standard deck of playing cards has 52 cards divided equally into four suits: hearts , diamonds , clubs , and spades . Within each suit, there are 13 cards: one ace, the numbers from 2 to 10, a jack, queen, and king.Suppose you are dealt a hand of 3 cards from a standard deck. In how many ways can this be done?How many of the sets will contain at least 1 ace among the 3 cards?What is the probability of at least 1 ace among the 3 cards you are dealt?

A poker hand is defined as drawing 5 cards at random without replacementfrom a deck of 52 playing cards. Find the probability of each of the following poker hands:(a) Four of a kind (four cards of equal face value and one card of a different value).(b) Full house (one pair and one triple of cards with equal face value).(c) Three of a kind (three equal face values plus two cards of different values).(d) Two pairs (two pairs of equal face value plus one card of a different value).(e) One pair (one pair of equal face value plus three cards of different values).

If one card is randomly selected from a well-shuffled standard deck of 52 cards, what is the probability that the card selected is not a heart?

2) How many different 13-card bridge hands contain a singleton in hearts and two five-card suits? [A5 marks](A singleton is exactly one card of a particular suit. A five-card suit is exactly five cards of the same suit.)

1a) How many different 4 card hands can be dealt from a deck of 52 cards?   *HINT 11b) How many different 4 card hands can be formed with at least 3 red cards? *HINT 21c) What is the probability of being randomly dealt a 4 card hand with at least 3 red cards? Round to at least 4 decimal places.1d) What is the probability of being randomly dealt a 4 card hand with less than 3 red cards?*HINT 3 Round to at least 4 decimal places.