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Twelve persons meet in a room and each shakes hands with all the others. The number of handshakes equals which count?
APermutations of 12 taken 2
BArrangements of 12 in order
CRepetitions of 12 taken 2
DCombinations of 12 taken 2
Answer & Solution
Correct answer: D. Combinations of 12 taken 2
1. X shaking hands with Y is the same event as Y shaking hands with X.
2. Order therefore does not distinguish one handshake from another.
3. So the count is the combinations of 12 different things taken 2 at a time.
_Source: NCERT Class 11 Mathematics, Ch 6 'Permutations and Combinations'_
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