Eight-dice-are-tossed-If-the-dice-are-identical-in-appearance-how-many-different-looking-distinguishable-occurrences-are-there-

Question Number 134389 by EDWIN88 last updated on 03/Mar/21

Eight dice are tossed . If the dice are identical in

appearance, how many different - looking

(distinguishable) occurrences are there ?

Answered by bramlexs22 last updated on 03/Mar/21

Theorem

If r is nonnegative integer, the number

of n - tupples (r_{1}, r_{2}, \dots, r_{n}), is r_{i} an

integer satisfying the condition

r_{i} ⩾ 0 (i = 1, 2, \dots, n)

r_{1} + r_{2} + r_{3} + \dots + r_{n} = r

is (\begin{matrix} n + r - 1 \\ n - 1 \end{matrix})

In this case \to {\begin{cases} n = 6 \\ r = 8 \end{cases}

so (\begin{matrix} 6 + 8 - 1 \\ 6 - 1 \end{matrix}) = (\begin{matrix} 13 \\ 5 \end{matrix}) = \frac{13.12.11.10.9}{5.4.3.2.1} = 1287