Exercises

1. How many permutations of the set begin with a and end

with c?

2. How many different messages can be sent by five dashes and three dots?

3. Roman has eight guests, two of whom are Jane and John. If the guests will arrive in a random order, what is the probability that John will not arrive right after Jane?

4. Find the number of distinguishable permutations of the letters MISSISSIPPI.

5. There are 20 chairs in a room numbered 1 through 20. If eight girls and 12 boys sit on these chairs at random, what is the probability that the thirteenth chair is occupied by a boy?

6. If we put five math, six biology, eight history, and three literature books on a bookshelf at random, what is the probability that all the math books are together?

7. Five boys and five girls sit in a row at random. What is the probability that the boys are together and the girls are together?

8. A man has 20 friends. If he decides to invite six of them to his birthday party, how many choices does he have?

9. A panel consists of 20 men and 20 women. How many choices do we have for a jury of six men and six women from this panel?

10. In a company there are seven executives: four women and three men. Three are selected to attend a management seminar. Find the following probabilities:

a) All three selected will be women.

b) All three selected will be men.

c) Two men and one woman will be selected.

d) One man and two women will be selected.

11. In a class of 18 students, there are 11 men and seven women. Four students are selected to present a demonstration on the use of the calculator. Find the probability that the group consists of the following:

a) All men

b) All women

c) Three men and one woman

d) One man and three women

e) Two men and two women.

12. A committee of four people is to be formed from six doctors and eight dentists. Find the probability that the committee will consist of the following:

a) All dentists

b) Two dentists and two doctors

c) All doctors

d) Three doctors and dentist

e) One doctor and three dentists

13. From a faculty of six professors, six associate professors, 10 assistant professors, and 12 instructors, a committee of size 6 is formed randomly. What is probability that

a) There are exactly two professors on the committee?

b) All committee members are of the same rank?

14. Almas has three sets of classics in literature, each set having four volumes. In how many ways can he put them in a bookshelf so that books of each set are not separated?

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