Multiple choice

A box contains $7$ red, $6$ white and $4$ blue balls. In how many ways can a selection of $3$ balls be made,i f none of the balls selected should be red?

  1. $135$
  2. $64$
  3. $50$
  4. $120$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total balls = 7 red + 6 white + 4 blue = 17. We need to select 3 balls, none red. This means selecting 3 from (6 white + 4 blue) = 10 balls. Ways = 10C3 = (10 * 9 * 8) / (3 * 2 * 1) = 120.

AI explanation

Since no red balls can be selected, the selection of 3 balls must be made from the 6 white and 4 blue balls. The total number of available non-red balls is 6 + 4 = 10. Using the combination formula, the number of ways to choose 3 balls from 10 is (10 choose 3), which equals 10 factorial divided by (3 factorial times 7 factorial), resulting in 120.

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