In how many ways can you seat 4 cats at Vasily's house? - briefly
The number of ways to seat 4 cats at Vasily's house can be calculated using permutations, as each cat is distinct and the order matters. There are 4! (4 factorial) possible arrangements, which equals 24 different seating options.
In how many ways can you seat 4 cats at Vasily's house? - in detail
The problem of determining the number of ways to seat 4 cats in Vasily's house can be approached using combinatorial mathematics, specifically permutations. A permutation is an arrangement of objects without repetition where order matters.
Firstly, consider that each cat is unique. If we were to seat the cats one by one, the first cat has 4 choices (any of the 4 seats), the second cat has 3 remaining choices, the third cat has 2 choices left, and the final cat has only 1 choice. This can be calculated using factorial notation:
[ 4! = 4 \times 3 \times 2 \times 1 = 24 ]
Thus, there are 24 different ways to seat 4 unique cats in Vasily's house if the order of seating is important.
However, if the cats are indistinguishable from each other (i.e., they look identical), then the problem simplifies because the order in which we seat them does not create a new arrangement. In this case, since all 4 cats are identical, there is only one unique way to seat them:
[ \frac{4!}{4!} = 1 ]
Therefore, the number of ways to seat 4 cats at Vasily's house depends on whether the cats are considered unique or indistinguishable. If they are unique, there are 24 different arrangements; if they are indistinguishable, there is only one way to seat them.