Please help, im so confused!

You draw five cards at random from a standard deck of 52 playing cards. What is the probability that the hand drawn is a full ho

Stels [109]

Answer:

The probability that the hand drawn is a full house is 0.00144.

Step-by-step explanation:

In a full house we have a hand that consists of two of one kind and three of another kind, i.e 5 cards are selected.

The number of ways of selecting 5 cards from 52 cards is:

${52\choose 5} = \frac{52!}{5!(52-5)!} \\=\frac{52!}{5!\times47!} \\=2598960$

In a deck of 52 cards there are 13 kind of cards, namely{K, Q, J, A, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

Two kinds can be selected in, ${13\choose 2}=\frac{13!}{2!\times(13-2)!} =\frac{13!}{2!\times11!} =78$ ways

One of the two kinds can be selected for 3 cards combination in ${2\choose 1} = 2$ ways.

There are 4 cards of each kind.

So 3 cards combination can be selected from any of the two kinds in ${4\choose 3} =\frac{4!}{3!(4-3)!} =4$ ways.

And 2 cards combination can be selected from any of the two kinds in ${4\choose 2} =\frac{4!}{2!(4-2)!} =6$ ways.

Thus, total number of ways to select a full house is:

${13\choose 2}\times{2\choose 1}\times{4\choose 3}\times{4\choose 2}\\=78\times2\times4\times6\\=3744$

The probability that the hand drawn is a full house is:

$\frac{Number\ of\ ways\ of\ Drawing\ a\ Full\ house)}{Number\ of\ ways\ of\ Selecting\ 5\ cards } =\frac{3744}{2598960} =0.00144$

Thus, the probability of playing a full house is 0.00144.

6 0

3 years ago

Order these numbers from least to greatest , 5.29 ,5.2912 , 5.029 , 5.8

Alona [7]

5.029, 5.29, 5.2912, 5.8

5 0

4 years ago

Read 2 more answers

What’s the slope I need help!

Lilit [14]

Answer:

-2\7 I think

Step-by-step explanation:

mafffffffffgfgggggfffs

3 0

3 years ago

Read 2 more answers

Alisha is drawing a map of her school. She is not able to draw the map to scale because it would be too large. Each centimeter o

arsen [322]

Here we want to see which one of the given graphs is the one with the correct relationship between distance in centimeters and meters. We will see that the correct option is the first graph.

<h3>Working with changes of scale.</h3>

So we know that each centimeter on the map must represent 4 meters in reality, this is a change of scale, so the scale is:

1cm = 4m

First, this relation is linear (each centimeter will always be equal to 4 meters) so the two bottom options that are not linear can be discarded, so we only have the first and second graph.

If you read them, you can see that in the second one 1 meter is equivalent to something near 5 cm, so this is also incorrect.

The only graph that shows a correct scale is the first one, where for each increment of 1 unit on the horizontal axis (the one in centimeters) we have an increase of 4 m (estimated). This means that 1cm = 4m, as in our change of scale.

So the correct option is the first graph.

If you want to learn more about changes of scale, you can read:

brainly.com/question/9302261

4 0

3 years ago

A. Name 3 different angles which could have a reference angle of 20 degrees. How did you arrive at this answer?.

IgorC [24]

Answer:

Answer:a. Since 20° is in the first quadrant, the reference angle is 20° .

Answer:a. Since 20° is in the first quadrant, the reference angle is 20° .b. Reference Angle: the acute angle between the terminal arm/terminal side and the x-axis. The reference angle is always positive. In other words, the reference angle is an angle being sandwiched by the terminal side and the x-axis. It must be less than 90 degree, and always positive.

Answer:a. Since 20° is in the first quadrant, the reference angle is 20° .b. Reference Angle: the acute angle between the terminal arm/terminal side and the x-axis. The reference angle is always positive. In other words, the reference angle is an angle being sandwiched by the terminal side and the x-axis. It must be less than 90 degree, and always positive.c. The rays corresponding to supplementary angles intersect the unit circles in points having the same y-coordinate, so the two angles have the same sine (and opposite cosines).

hopefully,

Zara♡

8 0

3 years ago