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

Question

The number of ways, 16 identical cubes, of which 11 are blue and rest are red, can be placed in a rowso that between any two red cubes there should be at least 2 blue cubes, is  (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

First we arrange 5 red cubes in a row and assume

x_{1}, x_{2}, x_{3}, x_{4}, x_{5}

and

x_{6}

number of blue cubes between them

Here,

x_{1} + x_{2} + x_{3} + x_{4} + x_{5} + x_{6} = 11

and

x_{2}, x_{3}, x_{4}, x_{5} \geq 2

So

x_{1} + x_{2} + x_{3} + x_{4} + x_{5} + x_{6} = 3

No.of solutions

=^{8} C_{5} = 56

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

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, x1​+x2​+x3​+x4​+x5​+x6​=11 and x2​,x3​,x4​,x5​≥2 So x1​+x2​+x3​+x4​+x5​+x6​=3 No.of solutions =8C5​=56