Multiple choice

Find the number of distinct throws which can be thrown with $n$ six faced normal dice which are indistinguishable among themselves

  1. $^{n+5}C_5$
  2. $(n+5)!$
  3. $^(n+6)C_6$

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

Since the dice are indistinguishable, only the counts of outcomes 1 through 6 matter. The number of nonnegative solutions to n1 + n2 + n3 + n4 + n5 + n6 = n is C(n+5,5).

AI explanation

When rolling n indistinguishable six-faced dice, the problem becomes one of distributing n identical items into 6 distinct boxes (the faces of a die). By the method of stars and bars, the number of non-negative integer solutions to x1 + x2 + x3 + x4 + x5 + x6 = n is given by the combination formula (n+6-1)C(6-1). This simplifies to n+5C5.

Keep practicing — related questions