Multiple choice

A box contains 10 red balls and 8 blue balls. In how many ways can 4 balls be selected if at least 2 of them must be red?

  1. 2,034

  2. 2,340

  3. 2,430

  4. 3,420

  5. 4,320
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total ways to select 4 balls from 18 = C(18,4) = 3060. Cases with 0 red: C(8,4) = 70. Cases with 1 red: C(10,1) * C(8,3) = 10 * 56 = 560. Total ways with at least 2 red = 3060 - (70 + 560) = 3060 - 630 = 2430.

AI explanation

Using the method of combinations, select exactly 2 red balls from 10 and 2 blue balls from 8, exactly 3 red and 1 blue, or exactly 4 red and 0 blue. The required number of ways is (10C2 times 8C2) + (10C3 times 8C1) + 10C4, which equals (45 times 28) + (120 times 8) + 210. The sum of 1260, 960 and 210 is 2430, so the answer is 2430.

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