Final Exam Answers
Math 351
July 28, 2005
Lim
1. If 5 cards are randomly selected from the standard 52-card deck, what
is the probability that they are all of the same suit?
5148/2598960
2. How many ways can 4 boys and 6 girls be lined up, if the boys must
be together?
120960
3. How many ways can 16 men be divided into three groups of respective
size 3,6,7?
960960
4. How many integer solutions does the following inequality have
x1+x2+x3+x4≤45
if the solutions must also satisfy x1≥0, x2≥1, x3≥2, x4≥1. (Hint:
Add another variable x5to make x1+·· · +x5= 45.)
148995
5. How many ways can a group of 3 students be chosen from a class of
40 students to work on a project?
9880
6. How many 4-letter English words are possible if all letters must be
different?
358800
7. How many 5-card poker hands are void in at least one suit?
1913496
8. An urn contains 4 white balls and 9 black balls. A ball is drawn at
random. What is the probability that it is white?
4/13
9. An urn contains 4 white balls and 9 black balls. Three balls are drawn
one by one without replacement. What is the probability that the
third ball is white?
4/13
1
