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How many ways are there to select 7 countries in the United Nations to serve on a council if 3 is selected from a block of 54, 1 are selected from a block of 66 and 3 are selected from the remaining 69 countries?

1 Answer

5 votes

Answer:

Total number of ways will be
=8.44727* 10^(10)ways

Explanation:

We have to select 7 countries

3 countries selected from a block of 54

So number of ways of selecting these three countries
=^(54)c_3=(54!)/(3!51!)=(54* 53* * 52* 51!)/(6* 51!)=24804ways

Now 1 country is selected from 66 block

So number of ways to select 1 country =
=^(66)c_1=(66!)/(1!65!)=(66* * 65!)/(1* 65!)=65ways

Now next 3 country is selected from 69 country

So
=^(69)c_3=(69!)/(3!66!)=(69*68* 67 * 66!)/(6* 66!)=52394ways

So total number of ways to select 7 countries = 24804×65×52394
=8.44727* 10^(10)ways

User Indradhanush Gupta
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