Question

A company plans to interview 23 recent graduates for possible employment. The company has four positions open. How many groups of four can the company select?

Answer 1

Answer:

8855

Step-by-step explanation:

Data provided in the question:

Number of graduate candidates to be interviewed = 23

Number of positions open = 4

Now,

Number of  groups that company can select = $^nC_r$

here,

n = total number of available choices = 23

r = number of individuals to be selected out of the given choices = 4

Thus,

Number of  groups that company can select = ²³C₄

= $\frac{23!}{4!(23-4)!}$

= $\frac{23\times22\times21\times20\times19!}{4\times3\times2\times1\times19!}$

= 8855