Question

A school director must randomly select 6 teachers to participate in a training session. There are 34 teachers at the school. In how many different ways can these teachers be selected, if the order of selection does not matter?

Answer 1

The selection of r object out of n, is carried out in C(n, r) many ways,

where
`C(n, r)= (n!)/(r!(n-r!))`

n! meaning 1*2*3*....*(n-1)*n


According to this, the selection of 6 teachers out of 34, can be carried out in C(34, 6) many different ways.


`C(34, 6)= (34!)/(6!(34-6!))=(34!)/(6!(28!))= (34*33*32*31*30*29*28!)/(6!28!)= (34*33*32*31*30*29)/(6!)`


`=(34*33*32*31*30*29)/(6*5*4*3*2*1)= 34*11*4*31*29=1,344,904`