Question

Three research departments have 10,6, and 9 members , respectively.each department is to select a delegate and an alternate to represent the department at a conference. In how many ways can this be done ?

Answer 1

`~~1.6xx10^14` ways

Explanation:

We have departments A, B, and C. Each one will send a delegate and an alternative, and so we'll have 2 people from each department. Order is important (1 will be the delegate and the other the alternate), and so this is a permutation problem:

`P_(n,k)=(n!)/((n-k)!); n="population", k="picks"`

We have:

`P_(10,2)P_(6,2)P_(9,2)=(10!)/(2!)(6!)/(2!)(9!)/(2!)=(3628800xx720xx362880)/6~~1.6xx10^14` ways