Multiple choice

There are $10$ balls of different colours. In how many ways is it possible to select $7$ of them, so as to include the red ball?

  1. 80

  2. 82

  3. 84

  4. 90
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To select 7 balls from 10 including the red ball, we must choose the red ball (1 way) and then choose 6 more balls from the remaining 9. This is calculated as 9C6, which is 9C3 = (9 * 8 * 7) / (3 * 2 * 1) = 84.

AI explanation

Because the red ball must be included in the 7 selected balls, you only need to choose the remaining 6 balls from the rest of the pool. From the total 10 balls, removing the 1 red ball leaves 9 balls. The number of ways to choose the remaining 6 balls is given by the combination formula 9C6. By the symmetry of combinations, 9C6 equals 9C3, which evaluates to 84.

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