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 long hair $\newline$ $3$ 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 long hair

\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 Brown Dogs: First, let's find out how many dogs are brown and have long hair. We know that $11$ dogs are brown.
Subtract Short Tails: Out of the $11$ brown dogs, we need to subtract the ones that have short tails. We know that $3$ brown dogs have short tails and not long hair, and only $1$ brown dog has both a short tail and long hair. $\newline$ So, $11 - 3 - 1 = 7$ brown dogs have long hair and do not have short tails.
Correct Subtraction: But wait, we made a mistake in the previous step. We shouldn't subtract the $3$ brown dogs with short tails and not long hair because we're looking for dogs with long hair. $\newline$ So, we should only subtract the $1$ brown dog that has both a short tail and long hair. $\newline$ So, $11 - 1 = 10$ brown dogs have long hair and do not have short tails.