Question

if seven squares are chosen at random on a chessboard the probability that they lie on a diagonal line is

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Asked on December 20, 2019 by

Deboshree Bhul

If four squares are chosen at random on a chess board, The probability that they lie on a diagonal line is =

64

C

4

91k

.Find the value of k

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ANSWER

S: We can select 4 square feet of 64 by

64

C

4

.

Now, for favourable number of cases there are 15 diagonals in each direction, but only 9 of them are long enough to contain 4 squares.

specifically, in each direction, there are two diagonals of length 4, two of length 5, two of length 6, two of length 7 and one of length 8.

So number of cases

=2{

4

C

4

+

5

C

4

+

6

C

4

+

7

C

4

}+

8

C

4

=2(1+5+15+35)+70=182

This is along one diagonal same this for another diagonal.

So total is 182+182=364

∴ Required probability =

64

C

4

364

∴ k=4