You select 6 cards randomly from a deck of 52 cards. What is the probability that all of the cards selected are face cards

Step-by-step explanation:

There are two different techniques that I can think of for arriving at the answer. The first method utilizes combination, sometimes referred to as the “choose” operator. First, we need to know how many 6 cards hands are possible, which can be calculated using 52 choose 6, which in notation looks like  (526)   =20,358,520 . This is our denominator.

Now that we know how many total 6 cards hands there are in a normal deck, we need to find the numerator, which is how many 6-card hands can be made up of all hearts. Since there are 13 hearts in the deck, we can find that number with  (136)   =1,716 .

Completely written out in mathematical notation, the probability of drawing 6 cards that are all hearts, appears as follows:

(136)(526)=171620358520≈0.0000843≈0.00843%  

The second method that results in the same value can be found by multiplying together the chances of drawing the individual cards at each step, for example, there is a  1352  chance of the first card drawn being a heart,  1251  for the second, and so on.

This second method looks like:

1352×1251×1150×1049×948×847≈0.0000843≈0.00843  

Incidentally,  13!46!7!52!  is another way to notate this second method.

Personally, I find the first method to be cleaner and easier to work with, but some may find the second more intuitive.

11/51

Step-by-step explanation: After you've picked the first card, if it's a face card then there are only 11 faces cards left, out of a total of 51. So the probability of the next card also being a face card is 11/51.

see below

step-by-step explanation:

7.   there are 10 data points in the set.   the middle point is between 5 and 6.   the middle point in the top half is 8   and the middle point in the bottom half is 3. to find the iqr , take point 8 and subtract point 3

mid term   point 8 = 100   point 3 = 88

iqr = 100-88 = 12

final   point 8 = 93   point 3 = 78

iqr = 93 - 78 = 15

the final has the greatest iqr

6.   b - there is a high data value that causes the data set to be asymmetrical for the males: the data for males are high and asymmetrical .   there is an outlier for the males that skews the data

5.   the   iqr is a better measure of spread for the movies and basketball games.   since the basketball game has an outlier, we do not want to use standard deviation for measurement.  

3.   the exam median is much higher than the class median.   the median line is farther to the right on the exams

2.   there is no way to tell what the means are from the box and whisker plots.  

you can first factor out the n to get n(1+5). we know that 1+5 is 6, so we just have 6n.