In an eight-cylinder 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. How many possible good firing sequences are there ?
A)40,320 sequences
B) 512 sequences
C) 576 sequences
D) 1,152 sequences
E) 24 sequences

Question

In an eight-cylinder 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. How many possible good firing sequences are there  ?
A)40,320 sequences
B) 512 sequences
C) 576 sequences
D) 1,152 sequences
E) 24 sequences

Quizplus · Accepted Answer

To alternate sides, the sequence must start with an odd-numbered cylinder (right side) and then an even-numbered cylinder (left side), continuing this pattern. There are 4 odd-numbered cylinders (1, 3, 5, 7) and 4 even-numbered cylinders (2, 4, 6, 8). The number of ways to arrange the odd cylinders is 4! (24 ways), and the number of ways to arrange the even cylinders is also 4! (24 ways). Therefore, the total number of good firing sequences is 4! * 4! = 576. However, since the sequence can start with either an odd or even cylinder, we multiply by 2, giving 2 * 576 = 1,152 sequences.

In an Eight-Cylinder Engine, the Even-Numbered Cylinders Are on the Left