A standard deck of cards is purchased, and the deck includes 3 jokers. This means if the jokers are included, the deck contains 5 5 cards. Teresa is playing a game in which she is dealt 8 cards from a deck that includes the jokers. What is the probability that Teresa's hand includes at least one joker?

The probability is

Step-by-step explanation:

We know that Teresa is playing a game in which she is dealt 8 cards from a deck that includes 3 jokers and 52 common cards (a total of 55 cards).

Let's define the following random variable :

: '' Number of jokers in the hand of Teresa ''

We need to find

This probability is equivalent to :

is the probability of having none jokers in the 8 card hand.

In order to find we are going to count all the cases in which (given that we are in presence of an equally - likely sample space)

We calculate as :

We define the combinatorial number

In the denominator we have which represents all the ways in which we can extract 8 cards from the deck of 55 cards.

In the numerator we have the product of  (which represents all the ways in which we can choose 8 cards from the 52 common cards) and    (which represents that from the total of 3 jokers we extract 0)

 If we perform the operation we find that :

Finally,

The probability is

none of the option is correct.

step-by-step explanation:

it says to find which expression equals 9^3 sqrt 10 = ?

9^3 sqrt 10 = 729 sqrt 10.

checking option a. 5 sqrt 10 + 4 sqrt 10

5 sqrt 10 + 4 sqrt 10

= 9 sqrt 10.

checking option b. 5^3 sqrt 10 + 4^3 sqrt 10

5^3 sqrt 10 + 4^3 sqrt 10

= 125 sqrt 10 + 64 sqrt 10

= 189 sqrt 10.

checking option c. 5 sqrt 10 + 4^3 sqrt 10

5 sqrt 10 + 4^3 sqrt 10

= 5 sqrt 10 + 64 sqrt 10

= 69 sqrt 10.

checking option d. 5^3 sqrt 10 + 4 sqrt 10

5^3 sqrt 10 + 4 sqrt 10

= 125 sqrt 10 + 4 sqrt 10

= 129 sqrt 10.

hence, none of the option is correct.

-2

7 - 9 = -2

reversed:

-2 + 9 = 7