by shivamtripathi22 | Jan 30, 2024 | Uncategorized
(Q). In how many ways batting order of 11 players can be made out of 15 players ? Sol:- First select then arrange. 11 Players can be selected out of 15 players in ¹⁵C₁₁ ways. Now these 11 players can be arranged in 11! ways. Hence total number of ways = ¹⁵C₁₁.11! ...
by shivamtripathi22 | Jan 21, 2024 | Uncategorized
(Q). In how many ways 15 students can be arranged in a row ?Sol:- 15 students can be arranged in a row in 15! ways Answer (Q). In how many ways 8 prizes from 1ˢᵗ to 8ᵗʰ can be given to a group of 8 students that includes 4 boys & 4 girls. Here a student can...
by shivamtripathi22 | Jan 21, 2024 | Uncategorized
(Q). In how many ways 5 distinct volume of chemistry and 7 distinct volume of Botany book can be arranged on a bookshelf such that no two chemistry books are together ?Sol:-•B₁•B₂•B₃•B₄•B₅•B₆•B₇•7 distinct botany books can be arranged in 7! ways. This will create 8...
by shivamtripathi22 | Jan 21, 2024 | Uncategorized
(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! ...
by shivamtripathi22 | Jan 21, 2024 | Uncategorized
(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...
by shivamtripathi22 | Jan 21, 2024 | Uncategorized
(Q). In how many ways can two squares be choosen on a 8×8 chess board such that they have only one corner...
by shivamtripathi22 | Jan 18, 2024 | Uncategorized
(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...
by shivamtripathi22 | Jan 18, 2024 | Uncategorized
(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...
by shivamtripathi22 | Jan 18, 2024 | Uncategorized
(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...
by shivamtripathi22 | Jan 16, 2024 | Uncategorized
(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...
