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

Rationale

Quantity A is greater.

To find the number of different groups of kittens and puppies, we use the combination formula, which calculates how many ways we can choose a subset from a larger set without regard to the order of selection. The number of ways to choose 2 kittens from 8 is greater than the number of ways to choose 6 puppies from 6.

A (Quantity A is greater.) CORRECT

Calculating the combinations, the number of ways to choose 2 kittens from 8 is given by \( \binom{8}{2} = \frac{8!}{2!(8-2)!} = \frac{8 \times 7}{2 \times 1} = 28 \). In contrast, the number of ways to choose 6 puppies from 6 is \( \binom{6}{6} = 1 \). Thus, Quantity A (28) is indeed greater than Quantity B (1).

B (Quantity B is greater.) YOUR ANSWER

For Quantity B, the only way to choose all 6 puppies from a total of 6 is one way, resulting in a count of 1. Since Quantity A is 28, this choice incorrectly suggests that Quantity B can outnumber Quantity A, which it cannot.

C (The two quantities are equal.) YOUR ANSWER

This option states that both quantities are the same, which is incorrect as the calculations show that Quantity A equals 28 while Quantity B equals 1. Therefore, they are not equal.

D (The relationship cannot be determined from the information given.) YOUR ANSWER

This option implies uncertainty in the comparison of the two quantities, which is not the case. The values derived from the combinations provide a clear relationship, showing that Quantity A is definitively greater than Quantity B.

Conclusion

In summary, by employing the combination formula, we find that the number of ways to select 2 kittens from 8 is significantly greater than the only way to select all 6 puppies from 6. Thus, Quantity A exceeds Quantity B, affirming that the relationship is clearly established.

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

Quantity A is greater.

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