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 from the remaining 69 countries?

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windyyork windyyork · Answer 1 · 2019-11-22T06:51:39+01:00

Answer: There are 2346953264 ways to do so.

Step-by-step explanation:

Since we have given that

Total number of selected countries = 12

Number of selected countries from a block of 45 = 3

Number of selected countries from a block of 57 = 4

So, remaining number of selected countries from a block of 69.

So, 12-(3+4)=12-7=5

Now, we need to find the number of ways, so we will use "Combination" to select that number of countries.

So, it becomes.

[tex]^{45}C_3\times ^{57}C_4\times ^{57}C_5\\\\=14190\times 395010\times 4187106\\\\=2346953264[/tex]

Hence, there are 2346953264 ways to do so.