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In how many shortest ways can we reach from the point (0, 0, 0) to point(3, 7, 11) in space where the movement is possible only along het x-axis,y-axis, and z-axis or parallel to them and change of axes is permitted onlyat integral points. (An integral point is one, which has its coordinate asinteger.)

Answer» Correct Answer - `.^(21)C_(3)xx .^(18)C_(7)`
The total number of units to be covered is 3+7+11=21. A person can choose 3 units in `.^(21)C_(3)` ways. A person can choose 7 units from remaining 18 in `.^(18)C_(7)` ways. The rest 11 units can be chosen in 1 way.
Therefore, the total number of ways is `.^(21)C_(3)xx .^(18)C_(7)xx1`.


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