Six teachers and 12 students volunteer for a committee to discuss extra-curricular activities. How many committees of 5 people can be made if: a) there must be exactly 3 students on the committee b) there must be at least one teacher and at least one student on the committee (3 marks)

a)

b)

Step-by-step explanation:

From the question we are told that:

Number Teachers

Number Student

Number in committee

a) Generally the equation for exactly 3 students on the committee is mathematically given by

b) Generally the equation for at least one teacher and at least one student on the committee is mathematically given by

Total Ways-(no of ways of selection no teacher or student)

Where total Ways

Therefore

-362

step-by-step explanation:

(12)(4)+2(12)-34(12)+2(12)-3

  \/         \/         \/         \/

  48 +   24 -   408 + 24 - 3

      \   /               \   /

          72     -     432 - 3 = -363

the line of