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

Answer:

a)$X=3300$

b)$Y=7770$

Step-by-step 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

$Y=8568-^{6}C_0*^{12}C_5+^{12}C_0*^{6}C_5$

$Y=8568-798$

$Y=7770$