ill try to fill in my guesses my answers will be bolded

Problem 1 (2 pts.): Let S = {a, b, c}.

(a) List all the 2-permutations of S.

(b) List all the 2-combinations of S.

**(a) {a,b} {a,c} {b,c} ?**

**(b) {a,b} {b,a} {b,c} {c,b} ? (does {b,b} etc.. count in any of them?)**

Problem 2 (3 pts.): How many bit strings of length 12 contain

(a) exactly five 1’s?

(b) at most five 1’s?

© at least five 1’s?

**(a) C(12,5) (12 choose 5)**

(b) 1+12+(12!/2!10!)+(12!/3!9!)+(12!/4!8!)+(12!/5!7!)

© 2^12 - (1+12+ C(12,2) + C(12,3) + C(12,4) )

(b) 1+12+(12!/2!10!)+(12!/3!9!)+(12!/4!8!)+(12!/5!7!)

© 2^12 - (1+12+ C(12,2) + C(12,3) + C(12,4) )

Problem 3 (3 pts.): A group contains k men and k women.

(a) How many ways are there to arrange them in a row?

(b) How many ways are there to arrange them in a row if the men and

women alternate?

(a) no idea? but i'd guess just 2*K!?

(b) K! * K! * 2 = 2(K!)^2

(a) no idea? but i'd guess just 2*K!?

(b) K! * K! * 2 = 2(K!)^2

Problem 4 (3 pts.): A club has 25 members.

(a) How many ways are there to choose a committee consisting of 4

members?

(b) How many ways are there to choose a president, vice president,

secretary and treasurer if no person can hold more than 1 position?

(a) C(25,4) = 25!/21!4!=12650

(b) P(25, 4) = 25× 24×23×22 = 303600

(a) C(25,4) = 25!/21!4!=12650

(b) P(25, 4) = 25× 24×23×22 = 303600

Extra Problem (3 pts.) : How many ways are there for a horse race

with three horses to finish if ties are possible? (NOTE: Two or three horses

may tie.)

C(3; 3) = 1 where three horses tie.

(b)C(3; 2)C(1; 1) = 3 where two horses tie and one horse ranks second.

©C(3; 1)C(2; 2) + C(3; 1)C(2; 1)C(1; 1) = 9 where for one case one horse

ranks ¯rst and the other two horses tie. Or one horse ranks ¯rst and one

horse ranks second and one horse ranks third.

so 9+3+1 = 13

C(3; 3) = 1 where three horses tie.

(b)C(3; 2)C(1; 1) = 3 where two horses tie and one horse ranks second.

©C(3; 1)C(2; 2) + C(3; 1)C(2; 1)C(1; 1) = 9 where for one case one horse

ranks ¯rst and the other two horses tie. Or one horse ranks ¯rst and one

horse ranks second and one horse ranks third.

so 9+3+1 = 13

How do my answers look? some I guess, some I used interweb resources.

thx

**Edited by Mercenary(FH), 19 October 2009 - 05:01 PM.**