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QJEEM22Ma1d37: JEE Main 2022 Mathematics - Class 11 JEEM22Ma1d37 Solution: The number of ways, 16 identical cubes, of which 11 are blue…

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 Verified Solution

First we arrange 5 red cubes in a row and assume x1, x2, x3, x4, x5 and x6 number of blue cubes between them

JEE Main 2022 (Online) 27th June Morning Shift Mathematics - Permutations and Combinations Question 97 English Explanation

Here, x1+x2+x3+x4+x5+x6=11x_1+x_2+x_3+x_4+x_5+x_6=11 and x2,x3,x4,x5≥2x_2, x_3, x_4, x_5 \geq 2

So x1+x2+x3+x4+x5+x6=3x_1+x_2+x_3+x_4+x_5+x_6=3

No. of solutions =8C5=56={ }^8 C_5=56

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