Question

The number of ways, 16 identical cubes, of which 11 are blue and rest are red, can be placed in a row so that between any two red cubes there should be at least 2 blue cubes, is _________.

Answer 1

Correct Answer: 56

First we arrange 5 red cubes in a row and assume x₁, x₂, x₃, x₄, x₅ and x₆ number of blue cubes between them
Here we see, 
x₁ + x₂ + x₃ + x₄ + x₅ + x₆ = 11
also,
x₂, x₃, x₄, x₅ ≥ 2
Hence,
x₁ + x₂ + x₃ + x₄ + x₅ + x₆ = 3
Therefore ,
Number of solutions found = ⁸C₅ 
= 56