Answer to Question #103869 in Statistics and Probability for suresh

Question

Question : A team has devised five campaigns to use for a target audience over several months. A campaign cannot be repeated.
a. How many possible sequences of the campaigns are there, assuming every campaign is sent to everyone? State any assumptions you make.

b. (Extra credit) Given five periods in each of which a campaign can be run, how many possible sequences of the campaigns are there if any campaign can be skipped? Assume that we care about a time interval having a campaign. That is, 1 _ 2 3 4 is different from 1 2 _ 3 4 (where _ denotes no campaign run in that period).

Answer 1

a. $\{1,2,3,4,5\}$

$$5!=120$$

b. $\{1,2,3,4,5, \_\}$

The number of permutations of $6$ objects taken $5$ at a time is given by:

$${6! \over (6-5)!}=720$$