BTGmoderatorDC wrote:In how many different ways can a group of twelve people be split into pairs ?
A 105
B 132
C 10,395
D 11,880
E 665,280
Since there are 12 people, the first person selected can be paired with any of the 11 other people, yielding
11 POSSIBLE PAIRS.
Since 2 of the 12 people have been selected thus far, the number of people remaining = 12-2 = 10.
Since 10 people remain, the next person selected can be paired with any of the 9 other people, yielding
9 POSSIBLE PAIRS.
Since 2 of the 10 remaining people were just selected, the number of people remaining = 10-2 = 8.
Since 8 people remain, the next person selected can be paired with any of the 7 other people, yielding
7 POSSIBLE PAIRS.
Since 2 of the 8 remaining people were just selected, the number of people remaining = 8-2 = 6.
Since 6 people remain, the next person selected can be paired with any of the 5 other people, yielding
5 POSSIBLE PAIRS.
Since 2 of the 6 remaining people were just selected, the number of people remaining = 6-2 = 4.
Since 4 people remain, the next person selected can be paired with any of the 3 other people, yielding
3 POSSIBLE PAIRS.
Since 2 of the 4 remaining people were just selected, the number of people remaining = 4-2 = 2.
The last 2 people yield
1 additional pair.
To combine the blue options above, we multiply:
11*9*7*5*3*1 = 11*63*15 = a very large integer with a units digit of 5.
The correct answer is
C.
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