Multiple choice

From a group of 10 persons, in how many ways can a selection of 4 persons be made such that a particular person is always include?

  1. $40$
  2. $120$
  3. $84$
  4. $210$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If one person is always included, we need to choose 3 more from the remaining 9. Ways = 9C3 = (9 * 8 * 7) / (3 * 2 * 1) = 3 * 4 * 7 = 84.

AI explanation

Because one particular person must always be included, we pre-select that 1 person, leaving 3 more persons to choose from the remaining 9 people. Using the combination formula, the number of ways to choose these 3 people is calculated as 9C3. Calculating this gives 9 multiplied by 8 multiplied by 7, divided by 3 multiplied by 2 multiplied by 1, which equals 84.

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