When solving a literal equation, what is the trick for isolating a variable that appears more than once?
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Answer:
The number of complete award announcements possible are 19,554,575,040.
Step-by-step explanation:
Combination is the number of ways to select <em>k</em> items from <em>n</em> distinct items when the order of selection does not matters.
Whereas permutation is the number of ways to select <em>k</em> item from <em>n</em> items when order of selection matters.
The number of people entering this year is 22.
The number of ways to select 5 people for Grand Prize is, .
The remaining number of people is, 22 - 5 = 17.
It is provided that the other 5 are selected according to an order.
The number of ways to select other 5 winners is,
The total number of ways to select 10 winners of 22 is:
Total number of ways = 26334 × 742560 = 19,554,575,040.
We have the data set:
{79, 83, 82, 78, 79, 77, 80, 73, 82, 72}
This data set has 10 items.
To complete the data summary is helpful to sort the data:
{72, 73, 77, 78, 79, 79, 80, 82, 82, 83}
The minimum value is 72.
<em>The quartile divides the data set in 4 parts. </em>
<em>The first quartile is the value for which 25% of the data is below.</em>
<em>The second quartile is the value for which 50% of the data is below. The second quartile is equivalent to the median.</em>
<em>The third quartile is the value for which 75% of the data is below.</em>
In this data set, as its size is a even number, the quartile fall between two positions, so we will calculate the average of this numbers.
The first quartile will fall in the position 0.25*10=2.5. Then we can calculate the 1st quartile as the average between the 2nd and 3rd number of the data set.
This values are 73 (2nd position) and 77 (3rd position), so the average is:
We can repeat this with the other quartiles:
Then:
The first quartile is 75.
The median (second quartile) is 79.
The third quartile is 82.
The maximum value is 83.