Three squares of a chess board are chosen at | vedclass

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

Question

(a) Three squares can be chosen out of $64$ squares in ${}^{64}{C_3}$ ways. Two squares of one colour and one another colour can be chosen in two mutu

Vedclass · Accepted Answer

$\frac{{16}}{{21}}$

Vedclass · Answer

(a) Three squares can be chosen out of $64$ squares in ${}^{64}{C_3}$ ways. Two squares of one colour and one another colour can be chosen in two mutually exclusive ways :
$(i)$ Two white and one black and $(ii)$ Two black and one white. Thus the favourable number of cases
$ = {}^{32}{C_2} 	imes {}^{32}{C_1} + {}^{32}{C_1} 	imes {}^{32}{C_2}.$
Hence the required probability $ = \frac{{2\left( {{}^{32}{C_1}.{}^{32}{C_2}} ight)}}{{{}^{64}{C_3}}} = \frac{{16}}{{21}}.$

Three squares of a chess board are chosen at random, the probability that two are of one colour and one of another is

Similar Questions

A bag contains $8$ black and $7$ white balls. Two balls are drawn at random. Then for which the probability is more

A bag contains, $7$ different Black balls .and $10$ different Red balls, if one by one ball are randomely drawn untill all black balls are not drawn, then probability that this process is completed in $12 ^{th}$ draw, is equal to

From a group of $10$ men and $5$ women, four member committees are to be formed each of which must contain at least one woman. Then the probability for these committees to have more women than men, is

A bag contains $3$ white and $7$ red balls. If a ball is drawn at random, then what is the probability that the drawn ball is either white or red

A five digit number is formed by writing the digits $1, 2, 3, 4, 5$ in a random order without repetitions. Then the probability that the number is divisible by $4$ is