Question

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?

Answer 1

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`