Question

how many ways are there to select 12 countries in the United Nations to serve on a council if 3 are selected from a block of 45 , 4 are selected from a block of 57 and the others are selected form the remaining 69 countries ​

Answer 1

The value is
`Z = 6.299*10^(16) \ ways`

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

`\left 45} \atop {}} \right.C _3 = ( 45! )/( (45-3) ! 3!)`

`\left 45} \atop {}} \right.C _3 = 14190`

Generally the number of way of selecting 4 from a block of 57

`\left 57} \atop {}} \right.C _3 = ( 57! )/( (57-4) ! 4!)`

`\left 57} \atop {}} \right.C _3 = 395010`

Generally the number of way of selecting (12 - (4 + 3) = 5) from a block of 69

`\left 69} \atop {}} \right.C _5 = ( 69! )/( (69-5) ! 5!)`

`\left 69} \atop {}} \right.C _3 = 11238513`

The ways of selecting 12 countries in the United Nations serve on a council is mathematically represented as

`Z = 14190 * 395010* 11238513`

`Z = 6.299*10^(16) \ ways`