Question

Suppose we want to choose 5 objects, without replacement, from 10 distinct objects. (a) How many ways can this be done, if the order of the choices matters? (b) How many ways can this be done, if the order of the choices does not matter?

Answer 1

a) 30240 ways

b) 252 ways

Step-by-step explanation

This is a permutation and combination problem.

- Problems that require us to pick a number of stuff from a much larger group, with the order of picking important are permutation problems.

- Problems that require us to pick a number of stuff from a much larger group, with the order of picking unimportant are combination problems.

For this question, we are asked to pick 5 objects from 10 distinct objects.

a) Order of choice matters (Thiss is a permutation problem)

Number of ways = 10P5 = 10!/(10 - 5)! = (10!/5!) = 30240 ways

b) Order of choice does not matter (This is a combination problem)

Number of ways = 10C5 = 10!/[5!(10 - 5)!] = (10!/5!5!) = 252 ways

Hope this Helps!!!