OA Explanation

(5th 5th 5th) _ _ _ _ _ _ _

Since, there are \(10\) people and exactly \(3\) get down on 5th floor, there are \(^{10}C_3\) ways in which we can choose \(3\) people out of \(10\) for the same i.e. \(120\) ways

Now, rest \(7\) will have only \(11\) floor options, they can get down in \(11\) x \(11\) x \(11\) x \(11\) x \(11\) x \(11\) x \(11\) ways i.e. \(11^7\) ways

Col. A: \(120\) x \(11^7\)
Col. B: \(2.4\) x \(10^9\)

Col. A: \(120\) x \(11^7\)
Col. B: \(240\) x \(10^7\)

Dividing both sides by \(120\);

Col. A: \(11^7\)
Col. B: \(2\) x \(10^7\)

Dividing both sides by \(10^7\);

Col. A: \((\frac{11}{10})^7\)
Col. B: \(2\)

Col. A: \((1.10)^7\)
Col. B: \(2\)

Clearly, Col. A < Col. B

Hence, option B