There are 6 persons arranged in a row Another person has to shake hands with 3 of them so that he sh...........

Math and Mental Ability Permutation & Combination

There are 6 persons arranged in a row. Another person has to shake hands with 3 of them so that he should not shake hands with two consecutive persons. In how many distinct possible combinations can the handshakes take place?

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Explanation:

We just need to choose 3 persons out of 6, such that no two of them are together.
Number of ways to choose 3 out of 6 people, without any constraints = ⁶C₃= (6 × 5 × 4)/(3 × 2 × 1) =20
Number of ways to choose 3 out of 6 people, such that all of them are together = 4
Number of ways to choose 3 out of 6 people, such that two of them are together = 3 + 2 + 2 + 2 + 3 = 12
So, required answer = 20 – (4 + 12) = 4