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The company is hosting a seminar. As part of a policy to ensure multic 29 Oct 2021, 02:45
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41% (02:50) correct 59% (02:54) wrong based on 107 sessions

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The company is hosting a seminar. As part of a policy to ensure multicultural interaction, no two participants from same country can stay in same floor. A three floor cottage with two apartments on each floor is reserved for the guests. How many ways are there to accommodate two speakers from US, two from India, one from Russia , and one from Australia ?

A. 72

B. 240

C. 360

D. 480

E. 720
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The company is hosting a seminar. As part of a policy to ensure multic 29 Oct 2021, 09:51
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Bunuel
The company is hosting a seminar. As part of a policy to ensure multicultural interaction, no two participants from same country can stay in same floor. A three floor cottage with two apartments on each floor is reserved for the guests. How many ways are there to accommodate two speakers from US, two from India, one from Russia , and one from Australia ?

A. 72

B. 240

C. 360

D. 480

E. 720
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There are 6 apartments. 1 US speaker can be accommodated in 6 ways, in any one out of 6 apartment. The 2nd US speaker will be accommodated in 4 ways, except for same floor apartment. Now 2 apartments are fixed. 2 Indian speakers will be accommodated in 10 ways ( if there were no restriction, they would be accommodated in 4*3 ways. Now out of these 12 ways, there are 2 ways in which both are on same floor) . The remaining 2 speakers can be accommodated in 2*1 way.
Total ways - 6*4*10*2 = 480

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The company is hosting a seminar. As part of a policy to ensure multic 29 Oct 2021, 11:15
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Abhishekgmat87
Bunuel
The company is hosting a seminar. As part of a policy to ensure multicultural interaction, no two participants from same country can stay in same floor. A three floor cottage with two apartments on each floor is reserved for the guests. How many ways are there to accommodate two speakers from US, two from India, one from Russia , and one from Australia ?

A. 72

B. 240

C. 360

D. 480

E. 720

There are 6 apartments. 1 US speaker can be accommodated in 6 ways, in any one out of 6 apartment. The 2nd US speaker will be accommodated in 4 ways, except for same floor apartment. Now 2 apartments are fixed. 2 Indian speakers will be accommodated in 10 ways ( if there were no restriction, they would be accommodated in 4*3 ways. Now out of these 12 ways, there are 2 ways in which both are on same floor) . The remaining 2 speakers can be accommodated in 2*1 way.
Total ways - 6*4*10*2 = 480

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Could you please explain how you came to the solution of 10 ways for the accommodation of the 2 indian? I still don't get it...
THank you
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Abhishekgmat87
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The company is hosting a seminar. As part of a policy to ensure multic 29 Oct 2021, 12:06
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Abhishekgmat87
Bunuel
The company is hosting a seminar. As part of a policy to ensure multicultural interaction, no two participants from same country can stay in same floor. A three floor cottage with two apartments on each floor is reserved for the guests. How many ways are there to accommodate two speakers from US, two from India, one from Russia , and one from Australia ?

A. 72

B. 240

C. 360

D. 480

E. 720

There are 6 apartments. 1 US speaker can be accommodated in 6 ways, in any one out of 6 apartment. The 2nd US speaker will be accommodated in 4 ways, except for same floor apartment. Now 2 apartments are fixed. 2 Indian speakers will be accommodated in 10 ways ( if there were no restriction, they would be accommodated in 4*3 ways. Now out of these 12 ways, there are 2 ways in which both are on same floor) . The remaining 2 speakers can be accommodated in 2*1 way.
Total ways - 6*4*10*2 = 480

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Could you please explain how you came to the solution of 10 ways for the accommodation of the 2 indian? I still don't get it...
THank you
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2 US speakers places are fixed which is in different floors. Now there are 4 positions left, 2 of which in same floor. Total no of ways of accommodating 2 Persons will be 4*3 but the 2 Indians can’t be accommodated in same floor. No of ways in which they can be accommodated in same floor = 2 as there is only 1 floor where they can be accommodated in either apartments. Required no of ways = 12-2 = 10.
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The company is hosting a seminar. As part of a policy to ensure multic 29 Oct 2021, 18:30
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Given: The company is hosting a seminar. As part of a policy to ensure multicultural interaction, no two participants from same country can stay in same floor. A three floor cottage with two apartments on each floor is reserved for the guests.

Asked: How many ways are there to accommodate two speakers from US, two from India, one from Russia , and one from Australia ?

Number of ways in which 2 participants from US can stay = 6*4
Number of ways in which 2 participants form India can stay = 4*3 - 2 = 10
Number of ways in which 1 participant from Russia and 1 participant from Australia can stay = 2*1 = 2

Total number of ways in which 2 participants from US, 2 participants form India, 1 participant from Russia and 1 participant from Australia can stay = 6*4*10*2 = 480

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The company is hosting a seminar. As part of a policy to ensure multic 31 Oct 2021, 08:48
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To make it a bit simpler, I think we could use Permutation formula for both the US delegates and the Indian delegates, instead of using Permutation formula only in the case of Indian delegates.

So, the no of ways the US delegates can be accommodated is 6P2 - 3P2 (i.e. usually they can be accommodated in 6P2 ways but since they aren't allowed to stay in the same floor we subtract 3P2 from 6P2. Why 3P2 - Suppose the six rooms have nos 11,12 [first floor, two rooms], 21,22,31,32, the two US delegates can stay in each of the floors together in two ways e.g. Person 1 in 11 & Person 2 in 12 or vice versa. So, it is 3*2 which is nothing but 3P2).

Now, the Indian delegates can stay in 4P2 - 2P2 ways.

And then the other two people can stay in two ways in the remaining two rooms.

Therefore, it is (30-6)*(12-2)*2 = 480.
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The company is hosting a seminar. As part of a policy to ensure multic 18 Jun 2024, 10:58
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