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

Answer:

There are 436937109262510348800 ways to selected 12 countries.

Step-by-step 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.

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