Question

How many strings of 10 ternary digits (0, 1, or 2)are here that contain exactly two 0s, three 1s, and five 2s?

Short answer

The total number of strings are 2520 strings of 10 ternary digits

Step-by-step solution

Step 1: Use the formula for string factorial

Total number of arrangements of n objects if al are different = n!

If r! of them are same number of ways are given by

\(\begin{array}{l}\frac{{n!}}{{{n_1}!{n_2}!..{n_k}!}} = \frac{{n!}}{{r!}}\\r! = {n_1}!{n_2}!..{n_k}!\end{array}\)

The n! Is string length

r! are outcome of strings

Step 2: Solution of strings of 10 ternary digits

Let’s, applied r! and n! values,

Because if the element that is repeated is exchanged with the similar element at some other position, it does not create a new outcome.

In our case we have two 0s, three 1s, five 2s and the string length is 10

Here,

\(\begin{array}{l}n! = 10!\\r! = 2!,3!,5!\\\frac{{n!}}{{r!}} = \frac{{10!}}{{2!.3!.5!}}\\\frac{{n!}}{{r!}} = 2520strings\end{array}\)