In a (5)-step online process, each step has (3) options. No two consecutive steps can have the same option, and the first option is fixed as (1). How many processes are possible?

Correct answer: (16)

The direct answer is option A, 16. The first step is fixed as option 1, so it contributes only one possibility. At every later step, the option used immediately before cannot be repeated. Since there are three options in total, two choices remain at each of steps 2, 3, 4 and 5. The multiplication principle gives \(1\times2\times2\times2\times2=2^4=16\). Option A, 16, is correct. Option B, 24, would incorrectly treat the later choices as if three choices were always available. Option C, 32, also overcounts by giving too many choices after the first step. Option D, 48, is another overcount and does not apply the consecutive-repetition restriction. Notice that a choice may repeat after one intervening step; only adjacent equal choices are forbidden. Memory cue: fixed first step gives 1, and each following step gives 2.