1. In how many ways can offices of president, vice president, and secretary be filled from a group of 10 persons if any person can hold no more than one office?

2. In how many ways can 8 children be arranged in a straight line if one particular child must be the first one in line?

3. How many 7-digit telephone numbers can be formed using the digits 0 through 9? Notice that the first digit cannot be 0.

4. How many distinguishable permutations can be formed using all letter of ALABAMA? OHIO?

5. A lottery winner can choose 3 prizes from a total of 10 different prizes. How many different ways can he select his winnings?

6. How many ways may a committee of 1 foreman, 2 union stewards, and 2 union members be selected from a group of 5 foremen, 8 stewards, and 30 members?

7. In how many different ways can $1, $5, and $10 be distributed among 7 students if each student receives no more than one bill?

8. Six passengers get on a bus with 20 vacant seats. In how many different ways can they be seated?

9. How many different groups of four can be chosen from a 15 member boat club to row a 4-oar yawl?

10. A signal officer has 6 different colored flags. If the flags are displayed by hoisting them in a vertical position, how many different signals can be made using 4 flags at a time? 5 at a time? 6 at a time? 3 or more at a time?

11. Twelve students registering for a math course are to be assigned in equal numbers to three sections. How many different ways can this be done?

ANSWERS:

1. = 720             2. = 5040

3. = 9,000,000            4. = 210 = 12

5. = 120         6. = 60,900

7. = 210         8. = 27,907,200

9. = 1365         10. = 360, = 720, 6! = 720

= 120, 120 + 360 + 720 + 720 = 1920

11. = 34650