Question

If I deal seven cards from a standard deck of 52, what is the chance that I will get two triples (three of a kind) and one other card. For example, King of hearts, king of spades, king of clubs, ten of diamonds, ten of spades, ten of clubs, three of hearts.

Answer 1

Answer:

3.417 X $10^{-9}$

Explanation:

Dealing seven cards indicates that they are not being replaced. The chance o getting two triples and one other card is as follows:

P(king of hearts) = 4/52 = 1/13 This is because there are 4 kings in a deck of cards.

P(king of spades) = 3/51 = 1/17 This is because there are three kings left in the deck and 51 cards left in the deck

P(king of spades) = 2/50 = 1/25 reduced number of kings and cards

P(Ten of diamonds) = 4/49 There are four tens in the deck but there are only 49 cards there.

P(ten of spades) = 3/48 = 1/16 Reduced number of tens and cards

P(ten of clubs) = 2/47

P(Three of hearts) = 4/46 There are four threes in a now reduced deck.

P(three of a kind and one other card): (1/13)(1/17)(1/25)(4/49)(1/16)(2/47)(4/46)

numerators = 1 X 1 X 1 X 4 X 1 X 2 X 4 = 32

denominators = 13 X 17 X 25 X 49 X 16 X 47 X 46 = 9364919200

numerators/denominators = 32/9364919200 = 3.417 X $10^{-9}$

Answer 2

Answer:

0.02

Explanation:

Let the heart, h = 3 ⇒ 3/52 = 1/14

Spade, s = 10 ⇒ 10/52 = 5/26

Club, c = 10⇒ 5/26

Diamond, d = 10⇒ 5/26

Using, nCr * (h)∧r * (s)∧n-r * (c)∧n-r * (d)∧n-r

7C1 * (1/14)*(5/26)²*(5/26)²*(5/26)² = 0.02