a committee must be formed with 3 teachers and 6 students. if there are 11 teachers to choose from, and 10…

Explanation:

Step1: Calculate the number of ways to choose teachers

The number of ways to choose (3) teachers out of (11) is given by the combination formula (C(n,k)=\frac{n!}{k!(n - k)!}), where (n = 11) and (k=3). [C(11,3)=\frac{11!}{3!(11 - 3)!}=\frac{11\times10\times9}{3\times2\times1}=165]

Step2: Calculate the number of ways to choose students

The number of ways to choose (6) students out of (10) is given by the combination formula (C(n,k)=\frac{n!}{k!(n - k)!}), where (n = 10) and (k = 6). [C(10,6)=\frac{10!}{6!(10 - 6)!}=\frac{10\times9\times8\times7}{4\times3\times2\times1}=210]

Step3: Calculate the total number of ways to form the committee

By the multiplication principle, the total number of ways to form the committee is the product of the number of ways to choose teachers and the number of ways to choose students. [165\times210 = 34650]

Answer:

(34650)