a man, a woman, a boy, a girl, a dog, and a cat are walking down a long and wind

Question

a man, a woman, a boy, a girl, a dog, and a cat are walking down a long and winding road one after the other.
A) in how many ways can this happen if the dog immediately follows the boy?
B) in how many ways can this happen if the dog(and only the dog) is beteeen the man and the boy? a man, a woman, a boy, a girl, a dog, and a cat are walking down a long and winding road one after the other.
A) in how many ways can this happen if the dog immediately follows the boy?
B) in how many ways can this happen if the dog(and only the dog) is beteeen the man and the boy? a man, a woman, a boy, a girl, a dog, and a cat are walking down a long and winding road one after the other.
A) in how many ways can this happen if the dog immediately follows the boy?
B) in how many ways can this happen if the dog(and only the dog) is beteeen the man and the boy?

Explanation / Answer

(A) If the dog immediately follows the boy, then there are 5! = 120 such ways.

(B) If the dog(and only the dog) is beteeen the man and the boy, then order man-dog-boy as a single object to be put into a line with three others, we see that there are 4 ! possible lines. Similarly, there are 4 ! lines in which the boy, dog, and man appear in this order.

So, by the addition rule, there are 4 ! + 4 ! = 48 ways in which the dog (and only the dog) is between the man and the boy.

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