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19 Mar 2020, 02:55
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
39% (02:22) correct
61%
(02:37)
wrong
based on 88
sessions
History
Date
Time
Result
Not Attempted Yet
What is the number of ways in which 4 squares can be chosen at random on a chess board such that they lie on a diagonal line? (A diagonal line refers to not only the diagonals of the chessboard but rather to all diagonal lines possible on the chessboard)
A. 140
B. 182
C. 256
D. 364
E. 504
Are You Up For the Challenge: 700 Level Questions
A. 140
B. 182
C. 256
D. 364
E. 504
Are You Up For the Challenge: 700 Level Questions
19 Mar 2020, 03:26
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Bunuel
What is the number of ways in which 4 squares can be chosen at random on a chess board such that they lie on a diagonal line? (A diagonal line refers to not only the diagonals of the chessboard but rather to all diagonal lines possible on the chessboard)
A. 140
B. 182
C. 256
D. 364
E. 504
A. 140
B. 182
C. 256
D. 364
E. 504
Number of diagonals present in a chess board in each direction that can contain 4 squares are:
2 diagonals each of length 4 units, 5, 6, & 7 units and 1 diagonal of length 8 units
Total ways of selecting 4 squares so that they line in a diagonal in each direction = selecting 4 squares from each length
= \(2*4c_4 + 2*5c_4 + 2*6c_4 + 2*7c_4 + 8c_4\)
= \(2(1 + 5 + 15 + 35) + 70\)
= \(182\)
The same number of selections are possible for another direction also
--> Total selections = \(2*182 = 364\)
Option D
02 Sep 2020, 06:39
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Dillesh4096
Bunuel
What is the number of ways in which 4 squares can be chosen at random on a chess board such that they lie on a diagonal line? (A diagonal line refers to not only the diagonals of the chessboard but rather to all diagonal lines possible on the chessboard)
A. 140
B. 182
C. 256
D. 364
E. 504
A. 140
B. 182
C. 256
D. 364
E. 504
Number of diagonals present in a chess board in each direction that can contain 4 squares are:
2 diagonals each of length 4 units, 5, 6, & 7 units and 1 diagonal of length 8 units
Total ways of selecting 4 squares so that they line in a diagonal in each direction = selecting 4 squares from each length
= \(2*4c_4 + 2*5c_4 + 2*6c_4 + 2*7c_4 + 8c_4\)
= \(2(1 + 5 + 15 + 35) + 70\)
= \(182\)
The same number of selections are possible for another direction also
--> Total selections = \(2*182 = 364\)
Option D
Hi @Dilesh4096,
Can you please the logic behind classifying diagonal categories? From my understanding, there are 2 diagonals (left-to-right and right-to-left) with 8 squares in each direction.
Thanks
