A committee of 7 members is to be formed from a group of 6 teachers and 5 students. The committee must contain at least 3 teachers and at least 3 students. However, 1 specific teacher and 1 specific student refuse to serve on the committee together. The total number of ways to form the committee is

Step-by-step solution

Total number of ways to select 7 members with at least 3 teachers and at least 3 students without any restriction: Case 1: 4 teachers and 3 students Number of ways = ⁶C₄ ⁵C₃ = 15 10 = 150 Case 2: 3 teachers and 4 students Number of ways = ⁶C₃ ⁵C₄ = 20 5 = 100 Total unrestricted ways = 150 + 100 = 250 Now, we find the number of ways where the specific teacher and the specific student are both included in the committee. We must select 5 more members from the remaining 5 teachers and 4 students. To satisfy the overall