Question

Suppose we want to choose 5 objects, without replacement, from 13 distinct objects. (a) How many ways can this be done, if the order of the choices is not taken into consideration? (b) How many ways can this be done, if the order of the choices is taken into consideration?

Answer 1

A. 1, 287 ways

B. 154,440 ways

Explanation:

A. We want to choose 5 objects from a total 13, without considering the order in which they are chosen.

The correct way to do this is by using the combination formula since order is not considered;

Thus we have ; 13 C 5 read as 13 combination 5;

Mathematically, n C r is ; n!/(n-r)!r!

Thus, we have ;

13!/(13-8)!8! = 13!/5!8! = 1,287 ways

B. By considering order, we shall be using the permutation formula;

Mathematically n P r = n!/(n-r)!

Read as n permutation r;

Using the numbers involved, we have ; 13 P 5

= 13!/(13-5)! = 13!/8! = 154,440 ways