There are $28$ dogs in a Kennel. $11$ dogs are brown. $8$ dogs have short tails. $17$ dogs have long hair. Only $1$ dog is brown with a short tail and $3$ dogs have but are not brown. $3$ dogs are brown with short tails and not long hair. $\newline$ How many dogs are brown with long hair but do not have short tails?

Full solution

Q. There are

28

dogs in a Kennel.

11

dogs are brown.

8

dogs have short tails.

17

dogs have long hair. Only

1

dog is brown with a short tail and

3

dogs have but are not brown.

3

dogs are brown with short tails and not long hair.

\newline

How many dogs are brown with long hair but do not have short tails?

Total Dogs Count: question_prompt: How many dogs are brown with long hair but do NOT have short tails? $\newline$ Total dogs in the kennel are $28$ .
Brown Dogs Count: There are $11$ brown dogs.
Short Tails Count: $8$ dogs have short tails.
Long Hair Count: $17$ dogs have long hair.
Brown with Short Tail Count: $1$ dog is brown with a short tail.
Long Hair and Short Tail Count: $3$ dogs have long hair and short tails but are not brown.
Brown with Short Tail and No Long Hair Count: $3$ dogs are brown with short tails and do not have long hair. This means these $3$ are included in the $11$ brown dogs.
Brown with Long Hair and No Short Tail Count: To find the brown dogs with long hair but no short tail, we subtract the brown dogs with short tails from the total brown dogs, and then subtract the brown dogs with short tails and no long hair. So, $11 - 1 - 3$ .