There are 6 persons arranged in a row. Another person has to shake hands with 3 of them so that he should…
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?
3
4
5
6
Solution
Number the persons 1 to 6. We must choose 3 of them with no two adjacent. The valid combinations are {1,3,5}, {1,4,6}, {1,3,6} and {2,4,6}. Hence there are 4 ways.