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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.

User Hamishmcn
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Answer:

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

User Billaraw
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