Step-by-step explanation:
<u>Permutations</u>:
n<em>P</em><em> </em>r = n!/(n + r)!
<u>Combinations</u>:
<em>nCr</em> = n!/(n - r)!r!
c - combination
p - permutations
Since in both the problems they are looking for different groups, it is a combination problem. the order in which the people were selected in each group is not important, what is required are different groups.
<u>A.</u>
n = 51
r = 3
51<em>C</em><em> </em>3 = 51! / ((51 - 3) ×3!)
<em>51C</em><em>3</em><em> </em><em>=</em><em> </em><em>2</em><em>0</em><em> </em><em>8</em><em>2</em><em>5</em><em> </em>groups
<u>OR:</u>
<em><u>B</u></em><em><u>.</u></em>
Answer:
3. 314 student and 226 adult
4. x = 6.5, y = -0.5
Step-by-step explanation:
3. First we will take our information and make a system of equations:
is the number of adult tickets sold and 
is the number of student tickets sold.
From the second equation we can rearange it to be:
Then we can plug in our new value of to our first equation
We can then find by plugging in s to our second equation
4. It is mostly solved already. We can take the value of y from the first equation and plug it into the second to get:
Then plug our value of x into the first equation to get:
432/100 is 4.32
4.32x45 is 194.4
answer: $194.40
Because we know that the number in between x+6 and 2x-3 is 18, we can solve for x by doing (x+6+2x-3)/2=18. this simplifies to 3x+3=36, or x=11.
