Question

Suppose that a computer software company has 30

Answer 1

Answer: $\dfrac{30!}{6!(24)!}$

Step-by-step explanation:

Given : The total number of programmers in the company = 30

The company wants to select a group of 6 programmers to work on a  particular project.

Since the order of selecting them does not matters , therefore we use combinations.

The number of combinations of r things taken from n things is given by :-

$^nC_r=\dfrac{n!}{r!(n-r)!}$

here, n= 30 and r= 6

So the number of different ways to form they could select a group of 6 would be $^{30}C_{6}=\dfrac{30!}{6!(30-6)!}$

$=\dfrac{30!}{6!(24)!}\\\\=\dfrac{30\times29\times28\times27\times26\times25\times24!}{(720)24!}=593775$

i.e. Total ways =593775

In terms of factorials , the number of total ways to form they could select a group of 6 is $\dfrac{30!}{6!(24)!}$ .