Ten police officers patrol in pairs. Two officers have each patrolled with 5 other officers, four officers have patrolled with 3 others, two have patrolled with 2 others, and two have patrolled with
Only 1 other officer. How many different patrol pairs have there been?

Question

Quizplus · Accepted Answer

The total number of different patrol pairs can be calculated by adding the number of unique partners each officer has and dividing by 2 (since each pair is counted twice in this sum). The calculation is as follows: (2 officers * 5 partners + 4 officers * 3 partners + 2 officers * 2 partners + 2 officers * 1 partner) / 2 = (10 + 12 + 4 + 2) / 2 = 28 / 2 = 14.

Ten Police Officers Patrol in Pairs