There are three rooms in a Hotel: one single, one double and one for four persons. How many ways are there to house seven persons in these rooms ?

Correct Answer: 105

Explanation:

Choose 1 person for the single room & from the remaining choose 2 for the double room & from the remaining choose 4 people for the four person room,

Then, ⁷C₁x ⁶C₂x ⁴C₄

_{= 7 x 15 x 1 = 105}

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