select the correct answer.\nconsider the word...

# Explanation: ## Step1: Determine first - letter possibilities The word "pencil" has 6 letters. The first letter can't be N or L, so there are 4 choices (p, e, c, i) for the first - letter. ## Step2: Determine arrangements of remaining letters After choosing the first letter, there are 5 remaining letters. The number of arrangements of these 5 remaining letters is \(5!\) (the number of permutations of 5 distinct objects), and \(n!=n\times(n - 1)\times\cdots\times1\), so \(5!=5\times4\times3\times2\times1 = 120\). ## Step3: Calculate total arrangements By the multiplication principle, the total number of arrangements of the 6 - letter word with the given condition is \(4\times5!\). \[4\times5!=4\times120 = 480\] # Answer: B. 480