Multiple choice

In how many ways can 12 identical pencils be kept in 4 distinct pencil boxes such that no box is empty?

  1. 455

  2. 165

  3. 11880

  4. 4¹²
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the stars and bars formula for distributing n identical items into k distinct bins such that no bin is empty: C(n-1, k-1). Here, C(12-1, 4-1) = C(11, 3) = (11 * 10 * 9) / (3 * 2 * 1) = 165.

AI explanation

To distribute 12 identical pencils into 4 distinct boxes with no box empty, we use the stars and bars method for positive integers. The formula for distributing n identical items into r distinct groups is (n-1)C(r-1). Substituting the given values, we calculate 11C3, which is (11 * 10 * 9) / (3 * 2 * 1). This results in 165 ways.

Keep practicing — related questions