Question

A ternary string is an ordered string of characters which consists of digits (0,1, or 2). For example, the ternary string 2122010 consists of exactly 2 zero's, 2 one's and 3 two's; another ternary string meeting these conditions is 0021221. How many ternary strings are there with exactly 4 zero's, 3 one's and 6 two's?

Answer 1

The number of ternary strings is an illustration of combination

There are 6227020800 ternary strings with exactly 4 zero's, 3 one's and 6 two's

How to determine the number of strings

Assume the zero's, one's and the two's can take any position in the string

For a ternary string of exactly 4 zero's, 3 one's and 6 two's, the number of characters in the string is 13.

The first 4 zeros can take any of the 13, 12, 11 and 10th positions

The next 3 ones can take any of the 9, 8 and 7th positions

The remaining 6 twos can take any 6! positions

So, the number of strings is:

Strings = 13* 12 * 11 * 10 * 9 * 8 * 7 * 6!

Evaluate the products

Strings = 6227020800

Hence, there are 6227020800 ternary strings with exactly 4 zero's, 3 one's and 6 two's

Read more about combination and permutation at:

https://brainly.com/question/11732255