P(n, r) = n (n - 1) (n -2) ... (n - r + 1) = , for 0

1) How many ways can a panel of 6 people be arranged in a row of 6 chairs?

2) On a university campus there are 50 blue bikes, 30 red bikes, and 10 green bikes. How many ways can a bike rack with 10 slots be filled?

Combinations - r distinct objects are chosen from n distinct objects, but the order does not matter, .

3) For a given n and r, which is bigger: P(n, r) or ?

4) Ways to choose 3 balls from 20 balls that are uniquely labeled 1 to 20.

a) For the combination 1, 2, 3 list all the corresponding permutations that use the same balls:

b) For the combination 1, 2, 4 list all the corresponding permutations that use the same balls:

c) Develope a formula showing the relationship between P(n, r) and .

P(n, r) =

5) A U8 soccer team carries 8 players on the roster, 4 players may be on the field at one time. How many different combinations of players may be on the field at any one time?