
probability
4. Seven cards each containing one of the following letters C,B,T,A,E,M and H are placed in a hat. Each letter is used only once. Stu will pull four cards out at random and without replacement. what is the probability that Stu pulls out M,A,T,H in order?? express your answer as a common fraction.
5. If x and y are positive integers with x+y<40, what is the largest possible product xy?
6. Consider the rectangular region with vertices at (5,4), (5,4), (5,4) and (5,4). how many points with integer coordinates will be strictly in the interior of this rectangular region?
7. What is the degree measure of an interior angle of a regular pentagon?

polygon angles
You can figure out the value of any interior angle of a polygon by letting
n= the number of sides
180(n2)/n
For a pentagon
180(52)/5
=108 degrees

If x+y are 2 integers less than 40 but not equal to. Then their sum must be 39. If you take the 2 largest integers whose sum is 39, ie 19 and 20, their product will be 380. That should be your answer.

4. Seven cards each containing one of the following letters C,B,T,A,E,M and H are placed in a hat. Each letter is used only once. Stu will pull four cards out at random and without replacement. what is the probability that Stu pulls out M,A,T,H in order?? express your answer as a common fraction.
M,A,T,H should have the same probability as pulling out any other four letter combination with out replacement.
Therefore you have
(1/7) chance of pulling M
(1/6) chance of pulling A next
(1/5) chance for T next
(1/4) chance to pull H last
1/(7*6*5*4)= 1/840 chance of pulling M,A,T,H or any other specific four card combination without replacement