Question

How many ways are there to select 9 countries in the united nations to serve on a council if 2 is selected from a block of 54, 1 are selected from a block of 70 and 6 are selected from the remaining 65 countries?

Answer 1

There are 676,173,744,400 ways to select 9 countries for the United Nations council based on the given conditions.

Step-by-step explanation:

To calculate the number of ways to select countries for the council, we can use the concept of combinations. Here's how we can approach it:

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• We need to select 2 countries from a block of 54, which can be done in C(54, 2) ways.
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• We need to select 1 country from a block of 70, which can be done in C(70, 1) ways.
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• We need to select 6 countries from a block of 65, which can be done in C(65, 6) ways.
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To find the total number of ways to select the countries, we multiply the number of ways for each block:

C(54, 2) * C(70, 1) * C(65, 6)

Using the formula for combinations - C(n, r) = n! / ((n-r)! * r!) - we can calculate the number of ways:

C(54, 2) = 54! / ((54-2)! * 2!) = 54 * 53 / (2 * 1) = 1431

C(70, 1) = 70! / ((70-1)! * 1!) = 70 * 1 / (1 * 1) = 70

C(65, 6) = 65! / ((65-6)! * 6!) = 65 * 64 * 63 * 62 * 61 * 60 / (6 * 5 * 4 * 3 * 2 * 1) = 6724520

Now we can find the total number of ways:

1431 * 70 * 6724520 = 6724520 * 100470 = 676173744400