Question

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

Answer 1

Total possible ways to select 6 teachers from 34 teacher are
`^(34)C_6=1344904`.

Explanation:

It is given that total number of teachers at a school is 34.

The school director must randomly select 6 teachers to part in a training session.

`^nC_r=(n!)/(r!(n-r)!)`

Where, n is total possible outcomes and r is number of selected outcomes.

Total teachers = 34

Selected teachers =6

Total number of possible ways to select 6 teachers from 34 teacher is

`^(34)C_6=(34!)/(6!(34-6)!)`

`^(34)C_6=(34* 33* 32* 31* 29* 28!)/(6!(28)!)`

`^(34)C_6=1344904`

Therefore total possible ways to select 6 teachers from 34 teacher are
`^(34)C_6=1344904`.