If we assume that all possible poker hands (comprised of 5 cards from a standard 52 card deck) are equally likely, what is the probability of being dealt: a. a flush? (a hand is said to be a flush if all 5 cards are of the same suit. note that this definition means that straight flushes (five cards of the same suit in numeric sequence) are also considered flushes.) b. one pair? (this occurs when the cards have numeric values a, a, b, c, d, where a, b, c, and d are all distinct.) c. two pairs? (this occurs when the cards have numeric values a, a, b, b, c, where a, b and c are all distinct.) d. three of a kind? (this occurs when the cards have numeric values a, a, a, b, c, where a, b and c are all distinct.) e. four of a kind? (this occurs when the cards have numeric values a, a, a, a, b.)

See the attached photo for the calculations and answers

Step-by-step explanation:

The calculations and explanations are shown in the 3 attached photos below.

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .

i believe the answers 600m