JEE MAIN - Mathematics (2022 - 27th June Morning Shift - No. 19)
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
56
Explanation
First we arrange 5 red cubes in a row and assume
x1, x2, x3, x4, x5 and x6 number of blue cubes
between them
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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 $={ }^8 C_5=56$
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 $={ }^8 C_5=56$
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