From the same bag, how many ways are there to draw two non-blue balls?

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Multiple Choice

From the same bag, how many ways are there to draw two non-blue balls?

Explanation:
Counting unordered pairs of items from a group is about choosing combinations, where the order doesn’t matter. To draw two non-blue balls from the bag without replacement, you’re forming pairs of non-blue balls. If there are five non-blue balls in the bag, the number of ways to pick two of them is 5 choose 2, which equals 10. You can also see it by thinking: there are five choices for the first non-blue ball and four for the second, giving 5 × 4 = 20 ordered pairs; since AB and BA represent the same pair, divide by 2 to get 10. The blue balls don’t affect this count because we’re only counting the ways to select non-blue balls. Hence the correct total is 10.

Counting unordered pairs of items from a group is about choosing combinations, where the order doesn’t matter. To draw two non-blue balls from the bag without replacement, you’re forming pairs of non-blue balls.

If there are five non-blue balls in the bag, the number of ways to pick two of them is 5 choose 2, which equals 10. You can also see it by thinking: there are five choices for the first non-blue ball and four for the second, giving 5 × 4 = 20 ordered pairs; since AB and BA represent the same pair, divide by 2 to get 10.

The blue balls don’t affect this count because we’re only counting the ways to select non-blue balls. Hence the correct total is 10.

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