Question:
In each of its move, a pawn in a chess board can move one step either horizontally or vertically to its adjacent cell from its current position. If a pawn is initially located at the South-West corner cell of the chess board, then the number of ways it can reach the North-East corner cell with minimum number of moves, is
In each of its move, a pawn in a chess board can move one step either horizontally or vertically to its adjacent cell from its current position. If a pawn is initially located at the South-West corner cell of the chess board, then the number of ways it can reach the North-East corner cell with minimum number of moves, is
Show Hint
Shortest path problems on grids are solved using combinations:
\[
{}^{m+n}C_m
\]
where $m$ and $n$ are moves in the two directions.
Updated On: Jun 17, 2026
- ${}^{64}C_2$
- $2\times{}^{8}C_2$
- ${}^{14}C_7$
- ${}^{16}C_8$
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Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Concept:
A standard chessboard has:
\[
8\times8
\]
cells.
To move from the South-West corner to the North-East corner using minimum moves, the pawn must move:
\[
7
\]
steps horizontally and
\[
7
\]
steps vertically.
Total minimum moves:
\[
14
\]
The number of distinct arrangements of these moves is:
\[
{}^{14}C_7
\]
Step 1: Count horizontal and vertical moves.
To move from one corner to the opposite corner: Horizontal moves required: \[ 7 \] Vertical moves required: \[ 7 \] Hence total moves: \[ 7+7=14 \]
Step 2: Arrange the moves.
Among the $14$ moves, choose positions for the $7$ horizontal moves. Therefore: \[ \text{Number of ways} = {}^{14}C_7 \] Hence, \[ \boxed{{}^{14}C_7} \]
Step 1: Count horizontal and vertical moves.
To move from one corner to the opposite corner: Horizontal moves required: \[ 7 \] Vertical moves required: \[ 7 \] Hence total moves: \[ 7+7=14 \]
Step 2: Arrange the moves.
Among the $14$ moves, choose positions for the $7$ horizontal moves. Therefore: \[ \text{Number of ways} = {}^{14}C_7 \] Hence, \[ \boxed{{}^{14}C_7} \]
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