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 ______.

Step-by-step solution

Given, 4 blue & 5 red spherical ball Now according to question there should be minimum 2 blue ball in between any two red ball. So assume a , b , c , d , e , f are number of blue balls, So, a + b + c + d + e + f = 11   ......(i) Where b , c , d , e ⩾ 2 Now let b = b ' + 2 c = c ' + 2 d = d ' + 2 e = e ' + 2 So equation (i) becomes a + b ' + 2 + c ' + 2 + d ' + 2 + e ' + 2 + f = 11 ⇒   a + b ' + c ' + d ' + e ' + f = 3 Now total ways will be = &#