Answer:
a
[tex]n= 75, 582[/tex]
b
[tex]n= 2300[/tex]
c
[tex]n = 253[/tex]
Step-by-step explanation:
Generally the size of the sample sample space is mathematically represented as
[tex]n = \left N } \atop {}} \right. C_r[/tex]
Where N is the total number of objects available and r is the number of objects to be selected
So for a, where N = 19 and r = 8
[tex]n = \left 19 } \atop {}} \right. C_8 = \frac{19 !}{(19 - 8 )! 8!}[/tex]
[tex]= \frac{19 *18 *17 *16 *15 *14 *13 *12 *11! }{11 ! \ 8!}[/tex]
[tex]n= 75, 582[/tex]
For b Where N = 25 and r = 3
[tex]n = \left 25 } \atop {}} \right. C_3 = \frac{25 !}{(19 - 3 )! 3!}[/tex]
[tex]= \frac{25 *24 *23 *22 ! }{22 ! \ 3!}[/tex]
[tex]n= 2300[/tex]
For c Where N = 23 and r = 2
[tex]n = \left 23 } \atop {}} \right. C_2 = \frac{23 !}{(23 - 2 )! 2!}[/tex]
[tex]= \frac{23 *22 *21! }{21 ! \ 3!}[/tex]
[tex]n = 253[/tex]
