Answer:
The value is [tex]Z = 6.299*10^{16} \ ways[/tex]
Step-by-step explanation:
From the question we are told that
The number of countries is n = 12
Generally the number of way of selecting 3 from a block of 45
[tex]\left 45} \atop {}} \right.C _3 = \frac{ 45! }{ (45-3) ! 3!}[/tex]
[tex]\left 45} \atop {}} \right.C _3 = 14190[/tex]
Generally the number of way of selecting 4 from a block of 57
[tex]\left 57} \atop {}} \right.C _3 = \frac{ 57! }{ (57-4) ! 4!}[/tex]
[tex]\left 57} \atop {}} \right.C _3 = 395010[/tex]
Generally the number of way of selecting (12 - (4 + 3) = 5) from a block of 69
[tex]\left 69} \atop {}} \right.C _5 = \frac{ 69! }{ (69-5) ! 5!}[/tex]
[tex]\left 69} \atop {}} \right.C _3 = 11238513[/tex]
The ways of selecting 12 countries in the United Nations serve on a council is mathematically represented as
[tex]Z = 14190 * 395010* 11238513[/tex]
[tex]Z = 6.299*10^{16} \ ways[/tex]
