Dog Breeder

A dog breeder currently has 9 breeding dogs. 6 of the dogs have exactly 1 littermate, and 3 of the dogs have exactly 2 littermates. If 2 dogs are selected at random, what is the probability that both selected dogs are NOT littermates?

1)1/6
2)2/9
3)5/6
4)7/9
5)8/9



Explanation:
Assume there are 9 dogs ABCDEFGHI.

Out of which 6 dogs have exactly 1 littermate: we can represent the data as below


A has (B).
B has (A).
C has (D).
D has (C).
E has (F).
F has (E).

3 dogs have exactly 2 littermates: This can be represented as

G has (H and I).
H has (G and I).
I has (G and H).

Total number of littermate pairs are AB, CD, EF, GH, GI, and HI.

Total number of dogs selected from 9 dogs: 9C2 = 36.

P(littermate pair) = 6/36 = 1/6.

P(not a littermate pair) = 1 - 1/6 = 5/6.

The correct answer is C.

A dog breeder currently has 9 breeding dogs. 6 of the dogs have exactly 1 littermate, and 3 of the dogs have exactly 2 littermates. If 2 dogs are selected at random, what is the probability that both selected dogs are NOT littermates?

a. 1/6
b. 2/9
c. 5/6
d. 7/9
e. 8/9

Let's say that the 9 dogs are ABCDEFGHI.

6 dogs have exactly 1 littermate:
Let's say that A and B are littermates, C and D are littermates, and E and F are littermates.
This means:
A has 1 littermate (B).
B has 1 littermate (A).
C has 1 littermate (D).
D has 1 littermate (C).
E has 1 littermate (F).
F has 1 littermate (E).

3 dogs have exactly 2 littermates:
Let's say that G, H and I are all littermates of each other.
This means:
G has 2 littermates (H and I).
H has 2 littermates (G and I).
I has 2 littermates (G and H).

Total number of littermate pairs = 6:
AB, CD, EF, GH, GI, and HI.
Total number of pairs that can be formed from 9 dogs:
9C2 = 36.

P(littermate pair) = 6/36 = 1/6.
P(not a littermate pair) = 1 - 1/6 = 5/6.

The correct answer is C.

If the GMAT were to use the word littermate, a definition would be offered.