A drone flies along a 3-D lattice from corner (0, 0, 0) to corner (2, 2, 2), each move being one unit in the +x, +y or +z direction. How many shortest flight paths are there?

Question

Accepted Answer

90. A shortest path is a word with 2 x's, 2 y's and 2 z's: 6!/2! 2! 2!=90. (720 =6! treats like moves as different.)

A drone flies along a 3-D lattice from corner (0, 0, 0) to corner (2, 2, 2), each move being one unit in the + $x, + y$ or + $z$ direction. How many shortest flight paths are there?

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More Permutations & Combinations practice

A drone flies along a 3-D lattice from corner (0, 0, 0) to corner (2, 2, 2), each move being one unit in the +x,+y or +z direction. How many shortest flight paths are there?

Step-by-Step Solution

Master this topic in 30 minutes a day.

More Permutations & Combinations practice

A drone flies along a 3-D lattice from corner (0, 0, 0) to corner (2, 2, 2), each move being one unit in the + $x, + y$ or + $z$ direction. How many shortest flight paths are there?