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  • There are 7 cats in a shelter that need to be placed in 7 rooms, with one cat per room. If 3 of the rooms are unfit for 4 of the cats due to renovations, how many ways are there to place

There are 7 cats in a shelter that need to be placed in 7 rooms, with one cat per room. If 3 of the rooms are unfit for 4 of the cats due to renovations, how many ways are there to place the cats in the rooms?

Option: 1

120


Option: 2

144


Option: 3

122


Option: 4

132


Answers (1)

best_answer

To find the number of ways to place the 7 cats in 7 rooms, considering the constraint that 3 rooms are unfit for 4 cats, we can apply combinatorics.
First, let's consider the placement of the 3 remaining cats (since 4 cats cannot be placed in unfit rooms) into the 3 remaining rooms (which can accommodate any cat). The number of ways to place 3 cats in 3 rooms is given by 3 !

Next, we consider the placement of the 4 cats that cannot be placed in the unfit rooms. Since there are 4 cats and 4 rooms remaining, we can place these cats in the rooms in 4 ! ways.

Finally, we multiply the number of ways to place the remaining 3 cats (3!) by the number of ways to place the 4 cats that cannot fit into the unfit rooms (4!).

Therefore, the total number of ways to place the cats in the rooms is given by,

 

\begin{aligned} &3 ! \times 4 !=6 \times 24 \\ &3 ! \times 4 !=144 \end{aligned}

 

Hence, there are 144 ways to place the cats in the rooms, considering the constraint that 3 rooms are unfit for 4 of the cats.

Posted by

shivangi.shekhar

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