Car Engines   In an eight-cylinder V8 engine, the even-numbered cylinders are on the left and the odd-numbered cylinders are on the right. A good firing order is a sequence of the numbers 1 through 8 in which right and left sides alternate.   (a) How many possible good firing sequences are there?  _________ firing sequences   (b) How many good firing sequences are there that start with a cylinder on the left?  __________ firing sequences

How many different license plates are possible if each contains 2 letters (out of the alphabet's 26 letters) followed by 3 digits (from 0 to 9)? How many of these license plates contain no repeated letters and no repeated digits? There are different possible license plates. (Simplify your answer.) There are different possible license plates if no letters or numbers are repeated. (Simplify your answer.) C

Task Assignments How many ways can an adviser choose 3 students from a class of 13 if they are each given a different task? There are ___ways an adviser can choose.

52. Shaking Hands in a Group A group of six strangers sat in a circle, and each one got acquainted only with the person to the left and the person to the right. Then all six people stood up and each one shook hands (once) with each of the others who was still a stranger. How many handshakes occurred?