Question

8. Four members of your school’s math/science department are needed for a party-planning committee. There are 4 math teachers, and 6 science teachers in the department.
9. 1. How many committees can be formed if there are no restrictions?
   2. How many committees have 2 math and 2 science teachers?
   3. How many committees have at least 1 math teacher and at least 1 science teacher?

Answer 1

4 math teachers, 6 science teachers

4 members committee

a) no restrictions

number of ways committees can be formed = .

number of ways committees can be formed =

number of ways committees can be formed = 10*3*7 = 210

b) 2 math teachers and 2 science teachers.

number of ways committees can be formed = .

number of ways committees can be formed =

number of ways committees can be formed = 6*5*3 = 90

c) atleast 1 math teacher and atleast 1 science teacher

if we subtract the number of ways a committee can be formed with no math teachers and number of ways a committee can be formed with no science teachers from total ways a committee can be formed, we get our answer

number of ways committees can be formed =   

number of ways committees can be formed =

number of ways committees can be formed = 10*3*7 - 3*5 - 1  ​​​​​​​  

number of ways committees can be formed =210 - 15 - 1​​​​​​​  ​​​​​​​  

number of ways committees can be formed = 194

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