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

Answer:

Total number of ways will be $=8.44727\times 10^{10}ways$

Step-by-step explanation:

We have to select 7 countries

3 countries selected from a block of 54

So number of ways of selecting these three countries $=^{54}c_3=\frac{54!}{3!51!}=\frac{54\times 53\times \times 52\times 51!}{6\times 51!}=24804ways$

Now 1 country is selected from 66 block

So number of ways to select 1 country = $=^{66}c_1=\frac{66!}{1!65!}=\frac{66\times \times 65!}{1\times 65!}=65ways$

Now next 3 country is selected from 69 country

So $=^{69}c_3=\frac{69!}{3!66!}=\frac{69\times68\times 67 \times 66!}{6\times 66!}=52394ways$

So total number of ways to select 7 countries = 24804×65×52394 $=8.44727\times 10^{10}ways$