(Q). In how many ways 15 students can be seated on 20 seats in a row ?Sol:- First select then arrange15 seats can be selected out of 20 seats in ²⁰C₁₅ ways. Now 15 students can be arranged in these 15 seats in 15! ways.Hence total number of ways = ²⁰C₁₅.15! ...
(Q). How many regular polygons can be formed by joining the vertices of a 36 sided regular polygon?Sol:- Since polygon is regular, so all its 36 vertices lie on a circle & are equidistant to its adjacent vertices.now consider 36 sided regular polygon.a new regular...
(Q). In how many ways two queens can be placed on a 8×8 chess board such that they are not able to attack each other (Queens can attack in the same row/column/diagonal)? (i). one queen is black & other queen is white (ii). both queens are identical. Solution:- we...
(Q). In how many ways two identical kings can be placed on a 8×8 chess board such that they are not on adjacent squares? Solution:- From the solution of previous question number of ways = 3612 (When kings are distinguishable) now in this question kings are...
(Q). In how many ways two kings one black & one white can be placed on a 8×8 chess board such that they are not on adjacent squares?Solution:- Here we have following cases for placing the 1ˢᵗ king.Case(i): Lets 1ˢᵗ king be placed at one of the 4 corners of chess...
(Q). Consider a decomposition of an 8×8 chessboard into p non overlapping rectangles with the following condition:- Condition (i):- Number of white and number of black squares are same Condition (ii):- If aᵢ is the number of white squares in the iᵗʰ rectangle then a₁...
(Q). Consider a 6×6 square which is dissected into 9 rectangles by lines parallel to its sides such that all the rectangles have integer sides. Out of 9 rectangles what is the maximum number of congruent rectangle ?Solution:-Let us solve this problem...
(Q). Consider 5 points in a plane are situated so that no two of the straight lines joining them are parallel, perpendicular, or co-incident. From each point perpendiculars are drawn to all the lines joining the other four points. Determine the maximum number of...
(Q). There are ‘n’ points in a plane. No three of which are on same straight line. All the possible straight lines are made by joining these ‘n’ points. (i) What is the maximum number of point of intersection of these straight lines? (ii)...
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