Permutations - Solve Counting Problems Worksheet
Number of Problems:
Determine the value:
1) How many numbers of 3 different digits can be formed from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9?
2) How many numbers of at most 3 different digits each can be formed from the digits 1, 2, 3, 4, 5, 6, 7, 8,9?
3) In how many ways can 4 boys and 3 girls be seated in a row containing seven seats
a) If they sit anywhere.
b) If the girls and boys must alternate.
4) A baseball manager insists on having his best hitter bat fourth and the pitcher bat last. How many batting orders are possible?
5) A language teacher wants to keep books of the same language together on his shelf. If he has 12 spaces for 5 French, 4 Italian, and 3 German books, in how many ways can they be placed on his shelf?
6) In how many ways can 8 people be seated around a table if 2 people insist of sitting next to each other?
7) How many license plates can be made using any two letters for the first 2 places and any of the numbers 0 through 9 for the last 3 given that no letter or number is repeated?
8) How many permutations are there of the letters of the word “Tennessee”?
9) In how many ways can 7 different colored beads be made into a bracelet?
10) Solve: P(n,5) = 20P(n, 3) for n.