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# At a wedding reception, twelve guests sat together at a round table. A

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Math Expert
Joined: 02 Sep 2009
Posts: 65765
At a wedding reception, twelve guests sat together at a round table. A  [#permalink]

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07 Jul 2020, 02:04
00:00

Difficulty:

45% (medium)

Question Stats:

71% (00:59) correct 29% (01:12) wrong based on 38 sessions

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At a wedding reception, twelve guests sat together at a round table. At the end of the meal, before they left, each guest at the table kissed all of the other guests goodbye. What was the total number of kisses?

A. 24
B. 55
C. 66
D. 78
E. 132

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At a wedding reception, twelve guests sat together at a round table. A  [#permalink]

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07 Jul 2020, 03:37
1
Total no. Of kisses = Sum of N-1 number of guests = sum of 11 positive number of guests
Sum = 11(11+1)/2
Sum = 11*12/2
Sum = 11*6
Sum = 66

Therefore total 66 kisses were been done at the table.

Alternatively,
Let the guests be 1,2,3,..........12

1 will kiss every other guest except himself.

(1,2)
(1,3),(2,3)
(1,4),(2,4),(3,4)
(1,5),(2,5),(3,5),(4,5)
(1,6),(2,6),(3,6)......,(5,6)
(1,7),(2,7),(3,7).......,(6,7)
(1,8),(2,8),(3,8).........,(7,8)
(1,9),(2,9),(3,9)..........,(8,9)
(1,10),(2,10),(3,10)........,(9,10)
(1,11),(2,11),(3,11).........,(10,11)
(1,12),(2,12),(3,12)..........,(11,12)
Total no. Of kisses = 11+10+9+8+7+6+5+4+3+2+1 = 66

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Re: At a wedding reception, twelve guests sat together at a round table. A  [#permalink]

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07 Jul 2020, 04:57
1
The round table is irrelevant. Every (unordered) pair of people creates one kiss, and we can pick 12C2 = (12)(11)/2! = 66 pairs of people, so that's the answer.
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Re: At a wedding reception, twelve guests sat together at a round table. A  [#permalink]

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07 Jul 2020, 06:58
Bunuel wrote:
At a wedding reception, twelve guests sat together at a round table. At the end of the meal, before they left, each guest at the table kissed all of the other guests goodbye. What was the total number of kisses?

A. 24
B. 55
C. 66
D. 78
E. 132

this question is similar to like having handshakes amongst a set of people
total possible exchange of kisses amongst 12 people ; 12c2 ; 66
OPTION C
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Re: At a wedding reception, twelve guests sat together at a round table. A  [#permalink]

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07 Jul 2020, 08:41
Step1: Understanding
Total people - 12
People required for a kiss - 2
As the order does not matter, the question is on combination

Step2: Calculation
Total number of kisses - 12C2 = 12!/10!*2! = 12*11/2 = 6*11 = 66
(D) is correct
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Re: At a wedding reception, twelve guests sat together at a round table. A  [#permalink]

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07 Jul 2020, 09:18
Bunuel wrote:
At a wedding reception, twelve guests sat together at a round table. At the end of the meal, before they left, each guest at the table kissed all of the other guests goodbye. What was the total number of kisses?

A. 24
B. 55
C. 66
D. 78
E. 132

Given: At a wedding reception, twelve guests sat together at a round table. At the end of the meal, before they left, each guest at the table kissed all of the other guests goodbye.
Asked: What was the total number of kisses?

Total number of kisses = 12C2 = 12*11/2 = 66

IMO C
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Re: At a wedding reception, twelve guests sat together at a round table. A  [#permalink]

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07 Jul 2020, 20:35
Bunuel wrote:
At a wedding reception, twelve guests sat together at a round table. At the end of the meal, before they left, each guest at the table kissed all of the other guests goodbye. What was the total number of kisses?

A. 24
B. 55
C. 66
D. 78
E. 132

Total number of kisses = 12C2 = 12*11/2 = 66

OA: C
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Re: At a wedding reception, twelve guests sat together at a round table. A   [#permalink] 07 Jul 2020, 20:35