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9. A committee of five teachers is to be chosen from six French teachers and six Music teachers. In how many ways can this be done so that the committee will consist of:

(a) Four French teachers
(b) At least one French teacher
(c) At most two Music teachers



Answer :

GinnyAnswer

Final answer:

Explained the different ways to form a committee with specific teacher requirements.


Explanation:

The committee can be chosen in different ways based on the requirements:

  1. Four French Teachers: 6 French teachers choose 4 = 6C4 = 15 ways.
  2. At least one French teacher: Choose 1 to 4 French teachers, then choose the rest from Music teachers = 6C1 6C4 + 6C2 6C3 + 6C3 6C2 + 6C4 6C1 + 6C5 6C0 + 6C6 6C0 = 186 ways.
  3. At most two Music teachers: Choose 0 to 2 Music teachers, then choose the rest from French teachers = 6C0 6C5 + 6C1 6C4 + 6C2 6C3 + 6C3 6C2 + 6C4 6C1 + 6C5 6C0 + 6C6 * 6C0 = 126 ways.

Learn more about Combinations and Permutations here:

https://brainly.com/question/34452834


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