Multiple choice

In a classroom of 20 students, in how many different ways can a study group of 7 students be formed?

  1. 38,360

  2. 77,520

  3. 79,250

  4. 87,520

  5. 97,275
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The number of ways to choose 7 students from 20 is given by the combination formula C(20, 7) = 20! / (7! * 13!) = (20 * 19 * 18 * 17 * 16 * 15 * 14) / (7 * 6 * 5 * 4 * 3 * 2 * 1) = 77,520.

AI explanation

To form a study group, we must select 7 students out of 20 without regard to order, which uses the combination formula nCr = n! / (r! (n-r)!). Calculating this gives 20C7 = 20! / (7! 13!). Expanding the factorials yields (20 19 18 17 16 15 14) / (7 6 5 4 3 2 1), which simplifies to 77,520.

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