Multiple choice

There are 6 black balls and 4 white balls in a box. In how many ways can 4 balls be selected, in which there is at least one white ball?

  1. 195

  2. 190

  3. 180

  4. 185

  5. 210
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A Correct answer
Explanation

Total ways to select 4 balls from 10 is 10C4 = 210. Ways to select 0 white balls (all black) is 6C4 = 15. Ways to select at least one white ball = Total - Ways with no white = 210 - 15 = 195.

AI explanation

Use the combinations formula to find the total ways to select 4 balls from the 10 balls, which is 10C4, giving 210 ways. Next, find the ways to select only black balls, which is 6C4, equal to 15 ways. Subtract the all-black selections from the total to get the selections with at least one white ball: 210 minus 15 equals 195.

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