Multiple choice

There are 6 black balls and 4 white balls in a box. Quantity A Number of ways to select 4 balls, in which there is at least one white ball Quantity B 195

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the given information.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total ways to select 4 balls from 10 is 10C4 = 210. Ways to select 4 balls with no white balls (all black) is 6C4 = 15. Ways with at least one white ball = 210 - 15 = 195. Quantity A = 195, Quantity B = 195. They are equal.

AI explanation

Use the complementary counting method to find the total ways to select 4 balls with at least one white ball from the 10 total balls. The total ways to pick any 4 balls is 10C4, which is 210, and the ways to pick only black balls is 6C4, which is 15. Subtracting the all-black selections from the total gives 210 minus 15 for 195 ways, making the two quantities equal.

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