Question

A trust has 25 members. In how many ways can a President, Vice President and a Secretary be selected?

Answer 1

From the 25 members a president can be selected in 25 ways

After the president is selected, 24 persons are left out.

So a Vice President can be selected in (from 24 persons) 24 ways.

After the selection of Vice President 23 persons are left out

So a secretary can be selected (from the remaining 23 persons) in 23 ways

So a president, Vice president and a secretary can be selected in ²⁵P₃ ways 

²⁵P₃ = 25 × 24 × 23 = 13800 ways