The organizers of a week-long fair have hired exactly nine security guards to patrol the fairgrounds at night for the duration of the event. Exactly four 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 4 guards will be available to patrol the fairgrounds on the following Saturday night? Choose the correct choice from the following answers: A) 3 B) 5 C) 7 D) 9 E) 11
For any given day, only the guards patrolling on the previous day won't be available. So, 4 guards who patrolled on Friday won't be available. We are thus left with 5 guards.   To choose 4 out of 5, we will have 5C4 = 5 different groups.   The answer is 5.
<result>B</result>
The organizers of a week-long fair have hired exactly nine security guards to patrol the fairgrounds at night for the duration of the event. Exactly four 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 4 guards will be available to patrol the fairgrounds on the following Saturday night?