Question

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)

Answer 1

a)
`X=3300`

b)
`Y=7770`

Explanation:

From the question we are told that:

Number Teachers
`T=6`

Number Student
`S=12`

Number in committee
`n=5`

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

`X=^(S)C_3*^(T)C_3`

`X=^(12)C_3*^(6)C_3`

`X=3300`

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

`T=^((6+12))C_5`

`T=8568`

Therefore

`Y=8568-^(6)C_0*^(12)C_5+^(12)C_0*^(6)C_5`

`Y=8568-798`

`Y=7770`