Combinations Worksheet

You may want to read Permutations and Combinations before doing this worksheet.

1. Evaluate:

   a. 8 C 5

   b. 9 C 3

   c. 9 C 6

   d. 7 C 7

   e. 5 C 3

2. Evaluate (¹⁹⁹⁹₁₀₀₀) − (¹⁹⁹⁹ ₉₉₉ )
3. In a class of thirty students, three are to be selected for the students' council. How many different ways are there of selecting these students?
4. In the game of poker, each player is dealt a hand of five cards. How many different poker hands are there?
5. In Lotto 6/49, six numbers are drawn out of a pool of 49. How many different combinations of the six winning numbers are there?
6. How many five-person committees can be selected from six men and eight women if there must be at least one woman included? (Very helpful hint: If there were no restrictions, how many committees would contain no women?)