JEE Main · 2026 · 06 Apr 2026 · Shift 2 · Permutations and Combinations

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A building has ground floor and 10 more floors. Nine persons enter in a lift at the ground floor. The lift goes up to the

1 0^{th}

floor. The number of ways, in which any 4 persons exit at a floor and the remaining 5 persons exit at a different floor, if the lift does not stop at the first and the second floors, is equal to :

(A)2184
(B)3064
(C)7056✓ Correct
(D)11340

Answer: (C)

Solution

The nine persons split into a group of

4

and a group of

5

(4 9) = 126

ways. Because the lift does not stop at the first or second floor, the two groups leave at two different floors chosen from floors

3

10

, that is

8

floors; choosing two of them and assigning one floor to each group gives

(2 8) \times 2 = 28 \times 2 = 56

ways. The total number of ways is

126 \times 56 = 7056

JEE Main · 2026 · 06 Apr 2026 · Shift 2 · Single correct option

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JEE Main · 2026 · 06 Apr 2026 · Shift 2 · Permutations and Combinations

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