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  4. In a 12 - storey house ten people enter a lift cabin. It is known that they will left in groups of 2, 3 and 5 people at different storeys. The number of ways they can do so if the lift does not stop to the second storey is

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Q. In a 12 - storey house ten people enter a lift cabin. It is known that they will left in groups of 2, 3 and 5 people at different storeys. The number of ways they can do so if the lift does not stop to the second storey is

Permutations and Combinations

Solution:

Leaving the ground floor and second floor, their are 10 floors in which three groups of people can left the lift cabin in $^{10}P_3$ ways, i.e. 720 ways.