If a(0, –1, 3) + b(1, 1, 1) – c(1, 2, 5) = (-2, 3, –8), determine a, b and c.

A family consisting of 2 parents and 3 children is to pose for a picture with 2 family members in the front and 3 in the back a. How many arrangements are possible with no restrictions? b. How many arrangements are possible if the parents must sit in the front? C. How many arrangements are possible if the parents must be next to each other?

In how many different ways can two letters be chosen from the letters A, B, C, D, E, F, and G? (The order of the two letters is not important.)

How many different signals can be sent, when three flags are used, if two of the 9 flags are missing?

A commuter must travel from Ajax to Barrie and back every day. Four roads join the two cities. The commuter likes to vary the trip as much as posible, so she alwaysleaves and returns by different roads. In how many different ways can she make the round-trip?