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As follows:

Oh yeah, I meant XYZ.

I am not too sure about the reflections part of it. 

First place a shell  down anywhere, call it A, now there are 9 shells left  so

9! takes into consideration of the rotation part

Maybe for the reflection you just divide by 2 becasue there is only one axis of symmetry through A

So maybe the answer is 9!/2

If you have access to the answers can you check and comment on whether this is the same.?

FIRSTLY Delphinia,  do not down vote answers just becasue you think it is wrong.

If a person makes a serious attempt at answering then you should thank them and not punish them in ANY way.

I answered you before I realiszed you had done this, otherwise I probably would not have answered you.

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Suppose 5 different integers are randomly chosen from between 20 and 69, inclusive. What is the probability that they each have a different tens digit?

there are  69-20+1= 50 numbers altogether

There are 5 different 10 digits,   2,3,4,5,6

Choose a number any number  prob = 1

now there are  49 numbers left and 40 of them have a tens unit not yet chose, 

P of the next one being a good choice is  40/49

and so on:

\(Prob = 1 * \frac{40}{49}*\frac{30}{48}*\frac{20}{47}*\frac{10}{46}\)

You can finish it. 

You are always welcome OldTimer  :))

(a) The probability is 3/10.

(b) The probability is 21/160.

B < C < D < A < E

The area of triangle ABC is 24 + 144*sqrt(3).

(a) There are 140 ways.

(b) There are 68 ways.

The probability is 7/180.

The probability is 4/17.

The other diagonal has length sqrt(148^2 - 24^2) = 4*sqrt(1333).

The point is (-6,18).

There are 72 ways.

The number of arrangements is 10!/(5!*5!) = 252.

The expected number of paths is 50/3.

Carissa's average speed is 140 meters per hour.

PQ = 8/5*sqrt(2)

What are all the squares and cubes between 1 and 10? Can you answer that? If you can, then you can solve the problem!.

Let the number of students = S

52%  -  40% = 12 % percentage rise as a reult of arrival of 15 freshmen.

12%S = 15

0.12S = 15

S=15 / 0.12 =125 - number of students at the dance after the arrival of 15 freshmen. 

If each person has 1, there are 20 - 5 = 15 stars and 5 - 1 = 4 bars. 

Can you take it from here?

a) Use stars and bars. There are 20 stars (stickers) and 5 - 1 = 4 bars

So, there are \({20 + 4 \choose 4} = \color{brown}\boxed{10,626}\) ways to choose.