Answer:
a gas in a rigid container has a pressure of 632 torrs and a temperature of 45 celsius. The pressure has increased to 842 torrs. What is the new temperature of the gas
A.
If we take 7 paintings to be hung in 7 spaces side by side, the first space can have any one of the 7 paintings, the second space can have any one of the remaining 6 paintings (as 1 is already hung), the third space can have any one of the remaining 5 paintings (as 2 already hung)...It goes on like this.
So we have
ways to arrange all the paintings from left to write. <em>(in factorial notation it is 7!=5040)</em>
B.
We use combinations rather than permutations because order doesn't matter. If we name the paintings A,B,C,D,E,F, and G, groups of 3 paintings of ABC or ACB are the same. So we evaluate
using the combination formula,

We have,

C.
This is similar to part A in some ways. Any 3 pictures can be arranged in
different ways.
. So, 6 different ways.
ANSWER:
A) 5040 ways
B) 35 different groups
C) 6 ways
V is about 1385.44 of the cylinder