- 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 $\newline$ but are not brown. $\newline$ - $3$ dogs are brown with short tail and NoT long hair. $\newline$ - How many dogs are brown with long hairl 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

\newline

but are not brown.

\newline

3

dogs are brown with short tail and NoT long hair.

\newline

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

Find Brown Dogs: First, let's find out how many brown dogs have long hair. We know there are $11$ brown dogs in total.
Identify Brown Dogs with Long Hair: Out of these, $1$ dog is brown with a short tail, and $3$ dogs are brown with a short tail but not long hair. So, we subtract these from the total brown dogs. $\newline$ $11 - 1 - 3 = 7$ dogs are brown and have long hair or short tails or both.
Determine Brown Dogs with Long Hair and No Short Tails: But we need to find the ones with long hair and without short tails. We know that only $1$ brown dog has a short tail, so we subtract this from the brown long-haired dogs. $\newline$ $7 - 1 = 6$ dogs are brown with long hair and do not have short tails.