The number of ways 16 identical cubes, of which 11 are blue and 5 are red, can be placed in a row such that between any two red cubes there are at least 2 blue cubes, is:

Question

Accepted Answer

56. With 5 red cubes there are 4 internal gaps and 2 ends (6 slots). Each internal gap must have at least 2 blue cubes, so reserve 4*2 = 8 blue cubes. Remaining blue cubes = 11 - 8 = 3. Distribute 3 identical blue cubes into 6 slots (stars and bars): C(3+6-1, 6-1) = C(8,5) = 56.

The number of ways 16 identical cubes, of which 11 are blue and 5 are red, can be placed in a row such that between any two red cubes there are at least 2 blue cubes, is:

Solution

Related JEE Advanced Maths questions