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CA Foundation · Quantitative Aptitude · Permutations and Combinations

In a hall in Delhi there are 12 people. Each pair shakes hands once, except that 4 of the people, who are all from one family, do not shake hands among themselves. What is the total number of handshakes?

There are 60 handshakes. With 12 people, 12C2 equals 66 possible pairs. The 4 family members would form 4C2 equal to 6 pairs that do not shake hands, so subtracting these 6 from 66 gives 60.

  1. A60Correct
  2. B66
  3. C62
  4. D56

Explanation

All pairs: 12C2 = 66. Pairs among the 4 family members: 4C2 = 6 are excluded. Handshakes = 66 − 6 = 60. The value 66 ignores the restriction.

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