Question

If 10 people apply for 3 jobs in how many ways can people be chosen for the jobs. 1. If the jobs are all the same. 2. If the jobs are all different. (please, please show work! Thank you!)

Answer 1

Answer:

1. 120 ways

2. 720 ways

Step-by-step explanation:

When the order is important, we have a permutation.

When the order is not important, we have a combination.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

$P_{(n,x)} = \frac{n!}{(n-x)!}$

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

1. If the jobs are all the same.

Same jobs means that the order is not important. So

3 from a set of 10.

$C_{10,3} = \frac{10!}{3!(10-3)!} = 120$

120 ways

2. If the jobs are all different.

DIfferent jobs means that the order matters.

$P_{(10,3)} = \frac{10!}{(10-3)!} = 720$

720 ways