Consider the 6 × 6 square in the figure. Let A 1 , A 2 , … , A 49 be the points of intersections (dots in the picture) in some order. We say that A i and A j are friends if they are adjacent along a r

Question

Consider the 6 × 6 square in the figure. Let A 1 , A 2 , … , A 49 be the points of intersections (dots in the picture) in some order. We say that A i and A j are friends if they are adjacent along a row or along a column. Assume that each point A i has an equal chance of being chosen. (There are two questions based on PARAGRAPH " II " , the question given below is one of them) Two distinct points are chosen randomly out of the points A 1 , A 2 , … … , A 49 . Let p be the probability that they are friends. Then the value of 7 p is

TestHub · Accepted Answer

Given,
We have to choose two distinct points randomly,
Now number of ways of selecting $2$ adjacent dots in row will be $= 6$ {as if you pick any dot then you have pick second dot from remaining $6$ dots, so total ways will be $1 \times {}^{6}C_{1} = 6$ }
Similarly, number of ways of selecting $2$ adjacent dots in column $= 6$
$∴$ Number of ways of selecting $2$ adjacent dots from the given diagram we will $= 6 \times 7 + 6 \times 7 = 84$
So, probability is given by,
$p = \frac{84}{{}^{49}C_{2}} = \frac{84 \times 2}{49 \times 48}$
$\Rightarrow 7 p = \frac{7 \times 84 \times 2}{49 \times 48} = \frac{1}{2} = 0.5$

Mathematics - Permutation & Combination Question with Solution | TestHub

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