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

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