Math 141, Sem. I, 1998-99 (R.A. Brualdi)
Handout 19 (November 11, 1998)
Topic: Hand-in # 6 (10 points per problem), Friday, November 13.


1. Consider the flag of the USA, with its 13 stripes, alternating red and
white in color, and 50 stars all white on a blue background. 

(a) If the stripes could be colored red and white in any way whatsoever, how
many different possible flags are there?



(b) If the stripes could be colored red and white in any way whatsoever but
exactly five must be red, how many different possible flags are there?



(c) If the stars could be colored white or green in any way whatsoever (but
the stripes alternate red and white), how many different possible flags are
there? 



(d) If the stripes could be colored red and white in any way whatsoever, and 
the stars could be colored white or green in any way whatsoever, how many
different flags are possible?




2. A basketball coach has 15 players on her roster, but a team on the field
consists only of five players.

(a) How many different teams can the coach field?


(b) If a team consist of one center, two forwards, and two guards, and the
roster contains 3 centers, 6 guards, and 6 forwards, how many different teams
can the coach field?


(c) If the roster contains 2 centers, 6 guards, 6 forwards, and 1 person who
can play either center or guard, how many different teams can the coach field?


(d) If the roster contains 2 centers, 6 guards, 6 forwards, and 1 person who
can play either center, guard, or forward, how many different teams can the
coach field?