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 ?
4
Starting from left to right, the person will be omitted standing next to the person shaking hand.
As the person shake hands with 3 so starting from left and shaking hands with first person we will omit the next one. Shaking hands with third person, the fourth person will be omitted.
So we have 4 persons left after omitting 2 and to find distinct possible combinations we will any 3 among them for handshakes
⇒ Number of distinct possible handshakes = \(\binom 4 3\)
= \(4!\over 3!\times 1!\) = 4
Hence, option 2 is correct.
Important Questions from Permutation and Combination
On a chess board, in how many different ways can 6 consecutive squares be chosen on the diagonals along a straight path ?
In a tournament of Chess having 150 entrants, a player is eliminated whenever he loses a match. It is given that no match results in a tie/draw. How many matches are played in the entire tournament?
The letters A, B, C, D and E are arranged in such a way that there are exactly two letters between A and E. How many such arrangements are possible?
There is a numeric lock which has a 3-digit PIN. The PIN contains digits 1 to 7. There is no repetition of digits. The digits in the PIN from left to right are in decreasing order. Any two digits in the PIN differ by at least 2. How many maximum attempts does one need to find out the PIN with certainty?
There are eight equidistant points on a circle. How many right-angled triangles can be drawn using these points as vertices and taking the diameter as one side of the triangle?
