Question

A string that contains only 0s,1s, and 2s is called a ternary string. How many strings of 10 ternary digits (0, 1, or 2) are there that contain exactly two 0s, three 1s, and five 2s? Generalize this to the number of ternary strings of length k with a 0’s, b 1’s, and c 2’s where a + b + c = k.

Answer 1

2520

Step-by-step explanation:

There are (10 2) ways to 0,'s whereas (8 3) ways to 1's and then location of then 2's are apply.

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10!/2!×3!×5!.

Answer 2

Number of strings = (10, 2)×(8,3) = 2520

Step-by-step explanation:

The number of possible combinations for taking two 0's is C(10, 2)

It remains 8 Positions

The number of possible combinations for taking three 1's is C(8,3)

So there remains 5 spots