The organizers of a week-long fair have hired exactly seven security guards to patrol the fairgrounds at night for the duration of the event. Exactly three guards are assigned to patrol the grounds every night, with no guard assigned consecutive nights. If the fair begins on a Monday, how many different groups of 3 guards will be available to patrol the fairgrounds on the following Saturday night? Choose the correct option
A) 3
B) 4
C) 5
D) 6
E) 7
For any given day, only the guards patrolling on the previous day won't be available. So, 3 guards who patrolled on Friday won't be available. We are thus left with 4 guards.   To choose 3 out of 4, we will have 4C3 = 4 different groups.   The answer is 4.
<result>B</result>
The organizers of a week-long fair have hired exactly seven security guards to patrol the fairgrounds at night for the duration of the event. Exactly three guards are assigned to patrol the grounds every night, with no guard assigned consecutive nights. If the fair begins on a Monday, how many different groups of 3 guards will be available to patrol the fairgrounds on the following Saturday night?