In the 2011 Canada general election, 166 Conservatives, 103 NDPs, 34 Liberals, 4 Bloc Quebecois, and 1 Green were elected. If an all party committee is to be formed consisting of 9 Conservatives, 5 NDPs, 2 Liberals, 1 Bloc Quebecois and 1 Green, how many different committees are possible?
C(166,9)*C(103,5)*C(34,2)*C(4,1)*C(1,1)≈ 4.15*10^25
I'm getting a different answer
7.13 × 10^16
To determine the number of different committees that can be formed with the given requirements, you need to use the concept of combinations.
Combinations express the number of ways to choose a specific number of objects from a larger set without considering their order.
In this case, we need to select 9 Conservatives, 5 NDPs, 2 Liberals, 1 Bloc Quebecois, and 1 Green out of their respective total numbers in the 2011 Canada general election.
Using the combination formula, the total number of different committees possible is:
C(166, 9) * C(103, 5) * C(34, 2) * C(4, 1) * C(1, 1)
Applying the formula:
C(n, r) = n! / (r! * (n-r)!)
C(166, 9) = 166! / (9! * (166-9)!)
= 166! / (9! * 157!)
Do similar calculations for the remaining combinations.
To accurately determine the number of different committees, you will need to calculate each combination individually and multiply them together.