Answer: [tex]\dfrac{30!}{6!(24)!}[/tex]
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 :-
[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
here, n= 30 and r= 6
So the number of different ways to form they could select a group of 6 would be [tex]^{30}C_{6}=\dfrac{30!}{6!(30-6)!}[/tex]
[tex]=\dfrac{30!}{6!(24)!}\\\\=\dfrac{30\times29\times28\times27\times26\times25\times24!}{(720)24!}=593775[/tex]
i.e. Total ways =593775
In terms of factorials , the number of total ways to form they could select a group of 6 is [tex]\dfrac{30!}{6!(24)!}[/tex] .
