Permutation and Combination
1. How many ways a president, vice-president and a secretary-treasurer for a high school Safe Grad committee be selected from 58 grade 12 students?
2. Abby walks 9 blocks from her home, H, to school, S. She always walks 5 blocks west and 4 blocks north. How many ways can Abby walk to school?
3. In how many ways 5 boys and 3 girls be seated around a table if
a. there is no restriction?
b. boy B1 and girl G1 are not adjacent?
c. No girls are adjacent?
4. Find the number of ways to sit n married couples around a table in each of the following cases:
a. Men and women alternate;
b. Every woman is next to her husband;
5. Five person entered the lift cabin on the ground floor of an 8 floor house. Suppose each of them can leave the cabin independently at any floor beginning with the first. The total number of ways in which each of the five persons can leave the cabin at any one of the 7 floors, is (75)
6. There are 6 teachers. Out of them 2 are primary teachers, 2 are middle teachers and 2 are secondary teachers. They are to stand in a row, so as the primary teachers, middle teachers and secondary teachers are always in a set. Then the number of ways in which they can do so is (48)
7. A telegraph has 5 arms and each arm is capable of 4 distinct positions, including the position of rest. What is the number of signals that can be made?
8. In how many ways can 20 students out of a class of 32 be chosen to attend class on a late Thursday afternoon (and take notes for the others) if
a. Paul refuses to go to class?
b. Michelle insists on going?
c. Jim and Michelle insist on going?
d. either Jim or Michelle (or both) go to class?
e. just one of Jim and Michelle attend?
f. Paul and Michelle refuse to attend class together?
9. A person has 8 children of them he takes 3 at a time to a circus. He does not take the same three children twice to the circus. How many times he will have to go to circus to ensure that every three children have seen the circus together? In this case find the number of times a particular child has visited the circus.
10. A man 7 relatives, 4 of them are ladies and 3 gentlemen, his wife has 7 relatives and 3 of them are ladies and 4 gentlemen. In how many ways can they invite a dinner party of 3 ladies and 3 gentlemen so that there are 3 of man's relative and 3 of wife's relatives?
11. A bit is either 0 or 1: a byte is a sequence of 8 bits. Find
a. the number of bytes that can be formed.
b. the number of bytes that begin with 11 and end with 11
c. the number of bytes that begin with 11 and do not end with 11 and
d. the number of bytes that begin with 11 or end with 11.
12. What is the number of diagonals that can be drawn in a polygon of n sides?
13. There are 25 true or false questions on an examination. How many different ways can a student do the examination if he or she can also choose to leave the answer blank?
14. In how many ways can 14 men be divided into six named teams, two with three players and four with two? In how many ways can 14 men be divided into two unnamed teams of three and four teams of two?
15. A chess tournament has 10 competitors, of which 4 are Russian, 3 are from the United States, 2 are from Great Britain, and 1 is from Brazil. If the tournament result lists just the nationalities of the players in the order in which they placed, how many outcomes are possible?