Question

How many ways are there to select 12 countries in the United Nations to serve on a council if 5 are selected from a block of 45, 4 are selected from a block of 57, and the others are selected from the remaining 69 countries? Briefly explain your answer.

Answer 1

There are 436937109262510348800 ways to selected 12 countries.

Explanation:

Let
`x_1, x_2, x_3, x_4,x_5` the countries selected from the block of 45. For
`x_1` there are 45 options of countries to select. For
`x_2` there are 44 options of countries to select because there can be no repeated countries. With the same reasoning, for
`x_3` there are 43 options, for
`x_4` there are 42 options and for
`x_5` there are 41 options.

Let
`x_6, x_7, x_8, x_9` the countries selected from the block of 57 countries. For
`x_6` there are 57 options of countries to select. For
`x_7` there are 56 options of countries to select because there can be no repeated countries. With the same reasoning, for
`x_8` there are 55 options and for
`x_9` there are 54 options.

Let
`x_(10), x_(11), x_(12)` the countries selected from the block of 69 remain countries. For
`x_(10)` there are 69 options of countries to select. For
`x_(11)` there are 68 options of countries to select because there can be no repeated countries and for
`x_(12)` there are 67 options.

For find the total of options o ways to select 12 countries we multiply the above options.

`45*44*43*42*41*57*56*55*54*69*68*67= 436937109262510348800`