1. A fair six-sided die is rolled six times. Which of the following is/are given by ${ }_{6} C_{2}\left(\frac{1}{6}\right)^{2}\left(\frac{5}{6}\right)^{4}$ ? A: The probability of getting exactly one 2 . B: The probability of getting exactly two $1 \mathrm{~s}$. $\mathrm{C}$ : The probability of getting exactly four $5 \mathrm{~s}$. D: The probability of getting exactly five $4 \mathrm{~s}$. E: The probability of getting exactly two scores less than 6 . F: The probability of getting exactly four scores greater than 1. [3]

Step 1 ：Analyze each option using the binomial probability formula with n = 6, k = 2, p = \(\frac{1}{6}\), and q = \(\frac{5}{6}\):

Step 2 ：A: Incorrect, as the expression represents getting exactly two successes.

Step 3 ：B: Correct, as getting two 1s and four non-1s matches the expression.

Step 4 ：C: Incorrect, as the expression represents getting exactly two successes.

Step 5 ：D: Incorrect, as the expression represents getting exactly two successes.

Step 6 ：E: Correct, as getting two scores less than 6 and four scores greater than or equal to 6 matches the expression.

Step 7 ：F: Correct, as getting four scores greater than 1 and two scores less than or equal to 1 matches the expression.

Step 8 ：\(\boxed{\text{B, E, F}}\)