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 only at integral points. (An integral point is one, which has its coordinate as integer.)

Answer

`.^(21)C_(3)xx .^(18)C_(7)`

Explanation

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`.