On a chess board, in how many different ways can 6 consecutive squares be chosen on the diagonals along a straight path ?
6
There are 2 diagonals with 8 squares each on the chess board and we have to choose 6 consecutive square.
We will assume block of 6 consecutive squares as one.
So we are left with 3 places on the chess board where it can be arranged by selecting any one of the place out of three i. e. 3C 1 = 3.
Similarly, for other diagonal too we will get 3 different ways
So, in total we have 6 different ways of choosing 6 consecutive squares.
Hence, option 2 is correct.
Important Questions from Permutation and 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 ?
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?
