In how many ways is it possible to choose a w | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) chess board has $32$ black and $32$ white squares.Total ways to choose one white and one black square $= {}^{32}C_{1} 	imes {}^{32}C_{1} = 32 	i

Vedclass · Accepted Answer

$768$

Vedclass · Answer

(D) chess board has $32$ black and $32$ white squares.Total ways to choose one white and one black square $= {}^{32}C_{1} 	imes {}^{32}C_{1} = 32 	imes 32 = 1024$.There are $8$ rows,and each row contains $4$ white squares and $4$ black squares.Ways to choose a white and a black square in the same row $= 8 	imes ({}^{4}C_{1} 	imes {}^{4}C_{1}) = 8 	imes 16 = 128$.Similarly,there are $8$ columns,and each column contains $4$ white squares and $4$ black squares.Ways to choose a white and a black square in the same column $= 8 	imes ({}^{4}C_{1} 	imes {}^{4}C_{1}) = 8 	imes 16 = 128$.Total ways where squares lie in the same row or column $= 128 + 128 = 256$.Therefore,the required number of ways $= 1024 - 256 = 768$.

In how many ways is it possible to choose a white square and a black square on a chess board so that the squares do not lie in the same row or column?

Similar Questions

Five balls of different colours are to be placed in three boxes of different sizes. Each box can hold all five balls. In how many ways can we place the balls so that no box remains empty?

If the permutations of $A, B, C, D, E$ taken all together are written down in alphabetical order as in a dictionary and numbered,then the rank of the permutation $DEBAC$ is

How many numbers lying between $10$ and $1000$ can be formed from the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ (repetition is allowed)?

$A$ teacher of a class wants to set $1$ question from each of $2$ exercises in a book. If there are $15$ and $12$ questions in the $2$ exercises respectively,then in how many ways can the $2$ questions be selected?

The number of ways in which the following prizes can be given to a class of $20$ boys,first and second Mathematics,first and second Physics,first Chemistry,and first English is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module