CMSC250, Fall 2003 Homework 11
Due Wednesday, November 19 at the beginning of your discussion section.
You must write the solutions to the problems single-sided on your own lined
paper, with all sheets stapled together, and with all answers written in sequential
order or you will lose points.
For these problems, you must simplify any permutations and/or combinations. That is, your
answers should only contain additions, subtractions, multiplications, divisions, exponents,
and factorials. Partial credit cannot be awarded unless your work is shown.
Recall that in the last homework, the CS professors formed a band and became rich and
famous. Well, the graduate TA’s became very jealous, so they decide to form their own
band.
1. If there are 25 graduate TA’s, how many ways can a group of 5 be selected to form a
band? (Note: this is ignoring which instrument each person plays.)
2. Of the 25 TA’s, 15 are men and 10 are women. How many ways can a band of 5 be
selected if there must be
(a) at least one woman?
(b) more women than men?
3. Of the 25 TA’s, 5 sing, 8 play guitar, 4 play bass, 6 play keyboards, and 2 play drums.
(a) How many 8-person bands can be formed if there must be 2 singers, 2 guitarists,
1 bassist, 2 keyboardists, and 1 drummer?
(b) How many 6-person bands can be formed if there must be exactly one drummer, at
least each one of each other instruments (guitar, bass, keyboard) and 0–3 singers?
(c) If the TA’s randomly select 6 people, what is the probability these 6 people fit
the criteria defined in part (b)?
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