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← JEE Main 2022 · 27 Jun · Shift 1
MathematicsInteger+4 / -1Question 24 of 90

JEE Main 2022 · 27 Jun · Shift 1, Mathematics question 24

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 and worked solution

Official answer: 56

Place the reds. Put 2 blues between each pair of the 5 reds: 8 blues used, 3 left.

Distribute the 3 spare blues into the 6 gaps: (3+55)=56\binom{3+5}5=56.

Answer: 56