Question

How many strings given 2 zeros and 3 1s?
A) 3
B) 5
C) 6
D) 7

Answer 1

There are 10 different strings that can be made with 2 zeros and 3 ones, which is calculated by using the permutations formula for arranging these items. The given answer choices do not contain the correct number, so all are incorrect.

Step-by-step explanation:

The question asks how many different strings can be created using 2 zeros and 3 ones. To solve this, we can use the concept of combinations in mathematics. Since the order in which we arrange the zeros and ones matters, we are dealing with permutations.

For n total items (numbers) of which p are the same kind (zeros) and q are another kind (ones), the number of permutations is given by the formula:

n! / (p! * q!)

Here, n = 2 + 3 = 5 (total number of digits), p = 2 (number of zeros), and q = 3 (number of ones).

Using the formula, we calculate:

5! / (2! * 3!) = (5 * 4 * 3 * 2 * 1) / ((2 * 1) * (3 * 2 * 1)) = 120 / (2 * 6) = 120 / 12 = 10.

Therefore, there are 10 different strings that can be made with 2 zeros and 3 ones, which is not listed in the given options. Thus, the provided options A) 3, B) 5, C) 6, and D) 7 are all incorrect.