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

\newline

11

dogs are brown.

\newline

8

dogs have short tails.

\newline

17

dogs have long hair.

\newline

- only

1

dog is brown with short tail and

\newline

3

dogs have short tail and long hair but are not brown.

\newline

3

dogs are brown with short tail and NoT long hair.

\newline

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

Find Dogs Count: First, let's find out how many dogs are brown and have long hair. We know that $11$ dogs are brown and $17$ dogs have long hair.
Subtract Dogs: We need to subtract the dogs that are brown with short tails and long hair, which is $1$ dog, and the dogs that are brown with short tails but not long hair, which is $3$ dogs. $\newline$ $11$ (brown dogs) $-$ $1$ (brown with short tail and long hair) $-$ $3$ (brown with short tail and not long hair) $=$ $7$ dogs.
Identify Remaining Dogs: Now, we have $7$ dogs that are brown and have long hair, but we don't know if they have short tails or not.
Correct Subtraction: Since we're looking for dogs that are brown with long hair but do NOT have short tails, we need to subtract the dogs that have short tails and long hair but are not brown, which is $3$ dogs. $\newline$ But we made a mistake in the previous step; we should not subtract these because we are only focusing on brown dogs.