If three smallest squares are chosen at rando | vedclass

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

Question

(B) chessboard has $8 	imes 8 = 64$ squares. The total number of ways to choose $3$ squares out of $64$ is $\binom{64}{3} = \frac{64 	imes 63 	imes

Vedclass · Accepted Answer

$\frac{1}{434}$

Vedclass · Answer

(B) chessboard has $8 	imes 8 = 64$ squares. The total number of ways to choose $3$ squares out of $64$ is $\binom{64}{3} = \frac{64 	imes 63 	imes 62}{3 	imes 2 	imes 1} = 41664$. To have $3$ squares together in a row, in each row of $8$ squares, there are $8 - 3 + 1 = 6$ ways to choose $3$ consecutive squares. Since there are $8$ rows, the total ways for rows is $8 	imes 6 = 48$. Similarly, for columns, there are $8$ columns and $6$ ways per column, so $8 	imes 6 = 48$ ways. The total number of favorable outcomes is $48 + 48 = 96$. The probability is $\frac{96}{41664} = \frac{1}{434}$.

If three smallest squares are chosen at random on a chess board, then the probability of getting them in such a way that they are all together in a row or in a column is

Similar Questions

Three mangoes and three apples are in a box. If two fruits are chosen at random,the probability that one is a mango and the other is an apple is

Four cards are drawn at random from a pack of $52$ playing cards. The probability of getting all four cards of the same suit is

If two sections of strengths $30$ and $45$ are formed from $75$ students who are admitted in a school,then the probability that two particular students are always together in the same section is

Four cards are drawn one by one from a well-shuffled pack of $52$ cards. What is the probability that all four cards belong to the same suit?

Let $X$ be a set containing $10$ elements and $P(X)$ be its power set. If $A$ and $B$ are picked up at random from $P(X)$ with replacement,then the probability that $A$ and $B$ have an equal number of elements is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module