Six stand-up comics, A,B,C,D,E, and F, are to perform on a single evening at a comedy club. The order of performance is determin
ed by random selection. Find the probability that a) comic E will be performed first
b) comic C will perform fifth and comic B will perform last
c) the comedians will perform in the following order D, E,C, A, B, F
d) comic A or comic B will perform first
<span>With no restrictions 6 comedians can perform in 6! = 720 ways
</span>E _ _ _ _ _ we can fill the 5 blanks with the 5 letters A,B,C,D,F in
5! = 120 ways
The probability of that is 120 ways out of 720 or 120/720 or 1/6.
b) comic C will perform fifth and comic B will perform last
_ _ _ _<span>C B
We can fill the 4 blanks with the 4 letters A,D,E,F in
4! = 24 ways.
The probability of that is 24 ways out of 720 or 24/720 or 1/30
</span>c) the comedians will perform in the following order D, E,C, A, B, F
<span>D E C A B F
There is just 1 way that can happen.
The probability of that is 1 way out of 720 or 1/720.
</span>d) comic A or comic B will perform first
_ _ _ A _ _<span> There are 5! = 120 ways to fill those 5 blanks with the letters B,C,D,E,F.
In addition to those, there are another 5! = 120 ways to fill these 5 blanks _ _ _ B _ with the letters A,C,D,E,F.
That's 2(5!) = 2(120) = 240 ways.
The probability of one of those is 240 ways out of 720 or 240/720 or 1/3.</span>
"<span>On Monday, Jason ran x miles. On Tuesday, he ran 5 fewer miles than on Monday.Which expression represents the total number of miles Jason ran over these two days?"
You can create a couple expressions to show the information: </span> <span> Hope this helps. -Benjamin
A triangular prism has three rectangular sides and two triangular faces. To find the area of the rectangular sides, use the formula A = lw, where A = area, l = length, and h = height. To find the area of the triangular faces, use the formula A = 1/2bh, where A = area, b = base, and h = height