MATH 141 InClass Exercise on Permutations and Combinations

Names_________________________________________________

1. Let A={a,b,c,d,e,f}. Write out all permutations of the elements of A taken two at a time. Then compute P(6,2).

2. Let A = {a,b,c,d,e,f}. Write out all three element subsets of A. Compute C(6,3).

3. A bag contains 6 red marbles and 4 green marbles. A set of three marbles is drawn from the bag at random.

a) How many different sets of three marbles can be drawn from the bag?______

b) How many sets of three red marbles can be drawn ? ________

c) Find the probability that the three marbles drawn are all red. P(Red)=________

d). Find P(Green) = ________

e) Find P(More Greens than Reds) = ________

f) Find P(Exactly one Green) = ________

4. A bag contains the letters{A, B, C, D, E, G, M, O}. Suppose that three letters are drawn in order and placed on the table to form a word. (The word does not have to be a word in English – it might be CDG, for example.)

a) How many different words are possible? _________

b) What is the probability that the word contains only consonants?

P(All Consonants) = ______

c) What is the probability that the word has a vowel as the middle letter and two consonants? P = ________

d) What is the probability of a word with exactly two vowels (in any position)?

P = ________

5. Write the fraction C(10,5)/C(20/10) in terms of factorials. Simplify the fraction as much as possible.

6. A committee of 5 is to be selected at random from a group of 10 English majors and 9 math majors. What is the probability that committee consists of 3 Math majors and 2 English majors?