[shahkb4]

Three persons enter in a lift at the ground floor. The lift will go upto $10^{\text {th }}$ floor.
The number of ways, in which the three persons can exit the lift at three different floors, if the lift does not stop at first, second and third floors, is equal to $\_\_\_\_$. [JEE MAIN 28 Jan 2026 S II]

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[shahkb4]

Solution

\[ \begin{aligned} & \text { available floors } \rightarrow 4^{\text {th }}, 5^{\text {th }}, \ldots 9^{\text {th }}, 10^{\text {th }} \\ & \text { Required ways }=\left({ }^{7} \mathrm{C}_{3}\right) 3!=\frac{765}{6} \times 6=7(30)=210 \text { Answer }(210) \end{aligned} \]

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