Multiple choice

There are infinite, alike, blue, red, green and yellow balls. Find the number of ways to select $10$ balls.

  1. $286$
  2. $84$
  3. $715$

  4. None of these.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

This is a stars and bars problem: selecting 10 items from 4 categories with replacement. Formula: (n + k - 1)C(k - 1) where n=10, k=4. (10 + 4 - 1)C(4 - 1) = 13C3 = (13 * 12 * 11) / (3 * 2 * 1) = 286.

AI explanation

This is a problem of combinations where we must find the number of ways to select 10 balls from 4 different colors, allowing for repetitions. By the stars and bars method, the formula for the number of combinations with repetition is (n + r - 1)Cr, where n is the number of types of items and r is the number of items to choose. Here, we have 4 types of balls and need to select 10, so we calculate (4 + 10 - 1)C10, which is 13C10. Evaluating 13C10 gives 286.

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