The question is an illustration of combination.
There are 5005 ways the volunteers can be selected
The given parameters are:
Since there is no restriction, as to who can be selected;
The total number of selection is calculated using the following combination formula
[tex]^nC_r = \frac{n!}{(n -r)!r!}[/tex]
Where:
[tex]n = 5 + 10=15[/tex]
[tex]r = 6[/tex]
So, we have
[tex]^{15}C_6 = \frac{15!}{9!6!}[/tex]
This gives
[tex]^{15}C_6 = 5005[/tex]
Hence, there are 5005 ways the volunteers can be selected
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