MDM 4U1
Permutations & Combinations
Review Sheet
Name:___________
1. Evaluate, showing ALL steps:
a)
7!
7!

2!5! 4!3!
b) 10P2 + 6P4
c)
812
  
 5 3 
2. Simplify, showing ALL steps:
(n  2)!
n!
a) (n  2)!
b) (n  1)!
3. Find the number of ways of arranging the letters of the word MATCHING if:
a. there are no restrictions;
b. the first letter must be M;
c. the odd numbered positions must remain unchanged;
d. the arrangement must end with NG.
4. In how many ways can the letters in the following words be arranged?
a. UNINTERESTING
b. SASKATCHEWAN
5. How many seven digit integers are there which include:
a. two 3s, three 2s and two 8s?
b. four 3s and three 4s?
6. How many digits greater than 200,000 are there using only the digits 1, 1, 1, 2, 2, 3?
7. From a
a.
b.
c.
deck of 52 cards, how many different 4 card hands could be dealt with:
two kings?
all red cards?
one card from each suit?
8. A developer will build 12 houses on the same side of Costly Court in a new subdivision. If he has
room for two houses modeled on Plan A, four modeled on Plan B and six modeled on Plan C, in how
many different ways can he arrange the houses on the street?
9. A committee of students and teachers is being formed to study the issue of student parking
privileges. 15 staff and 18 students have expressed an interest in serving on the committee. In
how many different ways could a 5 person committee be formed if it must include at least one
student and one teacher?
10. How many words can be formed using all the letters of the word SHRINKS if S must be directly in
front of H?
11. There are 5 speakers scheduled for a seminar on careers. How many different orders of speaking
are possible if:
a. there are no special conditions?
b. the marine biologist must speak first?
c. the electrical engineer and machinist are to speak one after the other?
d. the lawyer and doctor are not to follow one another in the program?
Answers:
1a) 56 b) 450
3a) 40,320
4b) 39,916,800
7c) 28,561
11c) 48
c) 12,320
b) 5,040
5a) 210
8) 13,860
11d) 72
2a) n(n-1)
c) 24
b) 35
9) 225,765
b)(n+2)(n+1)n
d) 720
6) 30
10) 720
4a) 129,729,600
7a) 6,768
b) 14,950
11a) 120
b) 24