JEE Main 2026 — Jan 28, Shift 2 — Mathematics solution

JEE Main2026Jan 28, Shift 2Mathematics

Three persons enter in a lift at the ground floor. The lift will go upto $1 0^{t h}$ 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 ______ .

Your answer

Solution

The available stopping floors are 4, 5, 6, 7, 8, 9, 10 — that is 7 floors.

Choose 3 distinct floors from these 7 and assign the three persons to them in some order: $(3 7) \times 3! = 35 \times 6 = 210$ .

(Equivalently, $^{7} P_{3} = 210$ .)

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