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# A hostess must seat 10 people around 2 circular tables.

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Manager
Joined: 17 Oct 2015
Posts: 107
Location: India
Concentration: Finance
Schools: ISB '18 (S)
GMAT 1: 690 Q47 V37
GMAT 2: 700 Q44 V41
WE: Corporate Finance (Commercial Banking)
A hostess must seat 10 people around 2 circular tables.  [#permalink]

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12 Mar 2016, 00:51
1
10
00:00

Difficulty:

65% (hard)

Question Stats:

57% (02:07) correct 43% (01:54) wrong based on 79 sessions

### HideShow timer Statistics

A hostess must seat 10 people around 2 circular tables. Table 1 can hold 6 people, table 2 can hold 4 people. If the hostess always seats people at Table 1 first and 2 seating arrangements are said to be different only when the positions of people are different relative to each other at the table, how many seating arrangements are possible?

A). 5*210
B). 15!*210
C). 120*3!
D). 5!*3!*210
E). 5!*5!*3!
Math Expert
Joined: 02 Aug 2009
Posts: 7102
Re: A hostess must seat 10 people around 2 circular tables.  [#permalink]

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12 Mar 2016, 08:03
2
debbiem wrote:
A hostess must seat 10 people around 2 circular tables. Table 1 can hold 6 people, table 2 can hold 4 people. If the hostess always seats people at Table 1 first and 2 seating arrangements are said to be different only when the positions of people are different relative to each other at the table, how many seating arrangements are possible?

A). 5*210
B). 15!*210
C). 120*3!
D). 5!*3!*210
E). 5!*5!*3!

Hi debbiem,

solve by taking one step at a time..
1)since there are two tables, the hostess has to choose 6 out of 10 and the remaining 4 will go to other table..
so WAYS= 10C6=10!/6!4!=210..
2)now 6 on the Table 1 can be seated in (6-1)! ways
3)and 4 on the Table 1 can be seated in (4-1)! ways

TOTAL ways=210*5!*3!
D

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Manager
Joined: 16 Jan 2017
Posts: 63
GMAT 1: 620 Q46 V29
Re: A hostess must seat 10 people around 2 circular tables.  [#permalink]

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12 May 2017, 07:40
chetan2u wrote:
debbiem wrote:
A hostess must seat 10 people around 2 circular tables. Table 1 can hold 6 people, table 2 can hold 4 people. If the hostess always seats people at Table 1 first and 2 seating arrangements are said to be different only when the positions of people are different relative to each other at the table, how many seating arrangements are possible?

A). 5*210
B). 15!*210
C). 120*3!
D). 5!*3!*210
E). 5!*5!*3!

Hi debbiem,

solve by taking one step at a time..
1)since there are two tables, the hostess has to choose 6 out of 10 and the remaining 4 will go to other table..
so WAYS= 10C6=10!/6!4!=210..
2)now 6 on the Table 1 can be seated in (6-1)! ways
3)and 4 on the Table 1 can be seated in (4-1)! ways

TOTAL ways=210*5!*3!
D

Can someone explain steps 2 and 3 please?
Manager
Joined: 08 Sep 2016
Posts: 115
Re: A hostess must seat 10 people around 2 circular tables.  [#permalink]

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12 May 2017, 09:23
vmelgargalan wrote:
chetan2u wrote:
debbiem wrote:
A hostess must seat 10 people around 2 circular tables. Table 1 can hold 6 people, table 2 can hold 4 people. If the hostess always seats people at Table 1 first and 2 seating arrangements are said to be different only when the positions of people are different relative to each other at the table, how many seating arrangements are possible?

A). 5*210
B). 15!*210
C). 120*3!
D). 5!*3!*210
E). 5!*5!*3!

Hi debbiem,

solve by taking one step at a time..
1)since there are two tables, the hostess has to choose 6 out of 10 and the remaining 4 will go to other table..
so WAYS= 10C6=10!/6!4!=210..
2)now 6 on the Table 1 can be seated in (6-1)! ways
3)and 4 on the Table 1 can be seated in (4-1)! ways

TOTAL ways=210*5!*3!
D

Can someone explain steps 2 and 3 please?

Because in a circular arrangement (using table 1 as an example) the seating arraignments for 123456 and 234561 are considered to be the same compared to a linear arraignment. Subtracting 1 removes the "double dipping".
Non-Human User
Joined: 09 Sep 2013
Posts: 9130
Re: A hostess must seat 10 people around 2 circular tables.  [#permalink]

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28 Jun 2018, 10:27
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Re: A hostess must seat 10 people around 2 circular tables. &nbs [#permalink] 28 Jun 2018, 10:27
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