13. The number of different groups of 2 kittens that can be chosen from a litter of 8 kittens, Quantity A. The number of different groups of 6 puppies that can be chosen from a litter of 6 puppies, Quantity B
Answer: A
Quantity A is greater.
The number of different groups of 2 kittens that can be chosen from a litter of 8 kittens is calculated using the combination formula, which shows that Quantity A is greater than Quantity B.
A) Quantity A is greater.
This option is correct because the number of ways to choose 2 kittens from 8 can be calculated using the combination formula \( C(8, 2) = \frac{8!}{2!(8-2)!} = 28 \). In contrast, the number of ways to choose 6 puppies from a litter of 6 is \( C(6, 6) = 1 \). Thus, 28 is greater than 1, making Quantity A greater.
B) Quantity B is greater.
This option is incorrect. The number of ways to choose 6 puppies from a litter of 6 is simply 1, as there is only one way to select all the puppies. Therefore, it cannot be greater than the 28 ways to choose 2 kittens from 8.
C) The two quantities are equal.
This option is incorrect. The calculations show that Quantity A (28 ways) is not equal to Quantity B (1 way). Since 28 is not equal to 1, this option does not hold.
D) The relationship cannot be determined from the information given.
This option is incorrect. The relationship can be determined with certainty based on the calculations of combinations for both quantities. There is sufficient information to conclude that Quantity A is greater than Quantity B.
Conclusion
The calculations definitively show that the number of ways to choose 2 kittens from 8 is significantly greater than the number of ways to choose 6 puppies from 6. Therefore, Quantity A is greater than Quantity B, confirming that option A is the correct choice while the other options fail to accurately represent the relationship between the two quantities.