A hospital board needs to form a medical task force consisting of 3 doctors and 3 nurses from an available pool of 7 doctors and 6 nurses. If one specific doctor and one specific nurse refuse to serve on the task force together, then the total number of ways to form the task force is _____.

Step-by-step solution

Total number of ways to select 3 doctors from 7 and 3 nurses from 6 without any restriction is ⁷C₃ ⁶C₃ = 35 20 = 700 The number of ways in which the specific doctor and the specific nurse are both selected requires choosing 2 more doctors from the remaining 6 and 2 more nurses from the remaining 5 . Number of such unfavorable selections is ⁶C₂ ⁵C₂ = 15 10 = 150 Therefore, the required number of ways to form the task force is 700 - 150 = 550 Answer: 550