The two senators from each of 10 American states prone to

Question

The two senators from each of 10 American states prone to hurricanes meet to discuss home insurance. They decide to choose 10 of themselves at random to form a committee to design a federal home insurance policy. If the probability that this committee will be made up of senators from 8 different states is n/20!, then n=


(A) 10!*10!/36 (B) 10!*10!*10!/36 (C) 10!*10!*10!/24 (D) 10!*10!*10!/45 (E) none of these

ps_dahiya · Answer

I can't understand the question. How many senators are there in one state. If 10 states have 1 each then there is only one combination to select 10 members.

kevincan · Answer

Silly me! Two senators per state, but this is not a civics class! My oversight!

ps_dahiya · Answer

Ways of selecting 10 people out of 20 = 20C10

Ways of selecting 8 states out of 10 states = 10C8

Ways of selecting 1 member each from 8 selected states = 2^8
Now ways of selecting 2 more members = 8C2
Total number o ways of selecting 10 people from 16 people of 8 states = 8C2 * 2^8
But wait. These contains duplicates. Half of these are duplicates.

Final Prob = (10C8 * 2^7 * 8C2)/20C10
 = 10! * 10! * 10! * 2/45 * 20!

so n = 10! * 10! * 10! * 2/45 i.e E

ps_dahiya · Answer

Taking an example of two set of two people each and we have to select 3 people with one from each set. we have

132
134
142
143 - Duplicate
231 - Duplicate
234
241 - Duplicate
243 - Duplicate

Am I wrong???

sgrover · Answer

This appears tobe a difficult problem.
Kevin has a good point. It will not be half always.

Lets consider 4 teams with 2 people each, and find the #ways in which 6 people can be selected such that every team has atleast 1 person from its team.

With your method it willbe : (2*2*2*2*4C2)/2 = 48
But, its easy to see that total#ways in which 6 people can be selected is 8C6 = 28 .. So the answer has to be less than 28 for sure.

The answer shd be: 8C6 - (#ways such that any of 3 teams has both the members represented)
=> 8C6 - 4C3 = 24

trivikram · Answer

Tomorrow is today :-D

. Please give the solution Thanks

kevincan · Answer

Number of ways of choosing 10 senators from 20= 20!/(10!)^2 (1)

2 states have 2 senators on the committee 10!/8!2!
Other 6 states have one senator 8!/6!2! *2^6

So, number of ways of making a committee of 20 from 8 states is 

10!*2^4/6! (2)

Probability = (2)/(1)= (10!)^3* 2^4/6! / 20!

So, n= (10!)^3/45   D

The two senators from each of 10 American states prone to

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