How many ways are there to select 9 countries in the United Nations to serve on a council if 1 is selected from a block of 60, 3 are selected from a block of 63 and 5 are selected from the remaining 66 countries?
Define n choose r as (n,r)=n!/(r!(n-r)!)
Then numnber of ways
=(60,1)*(63,3)*(66,5)
To determine the number of ways to select countries for the council, we need to calculate the product of the number of ways to select countries from each block.
For the first block, where 1 country is selected from a block of 60, there is only 1 way to select a country.
For the second block, where 3 countries are selected from a block of 63, we can use the combination formula. The number of ways to select r objects from a set of n objects is given by the formula:
C(n, r) = n! / (r!(n-r)!)
In this case, we need to calculate C(63, 3).
C(63, 3) = 63! / (3!(63-3)!) = 63! / (3!60!) = (63 * 62 * 61) / (3 * 2 * 1) = 39711
So, there are 39711 ways to select 3 countries from a block of 63.
For the third block, where 5 countries are selected from a block of 66, we can similarly calculate C(66, 5).
C(66, 5) = 66! / (5!(66-5)!) = 66! / (5!61!) = (66 * 65 * 64 * 63 * 62) / (5 * 4 * 3 * 2 * 1) = 133,852
Therefore, there are 133,852 ways to select 5 countries from a block of 66.
To find the total number of ways to select countries for the council, we need to multiply the number of ways to select countries from each block:
Total number of ways = 1 * 39,711 * 133,852 = 5,325,007,972
So, there are 5,325,007,972 ways to select 9 countries for the council.