Question

select the correct answer.
consider the word pencil. if all of the letters are used, and the first letter cant be n or l, how many ways can the letters be arranged?
a. 720
b. 480
c. 360
d. 96

Explanation:

Step1: Determine total letters and restrictions

The word "pencil" has 6 distinct letters. The first letter can't be N or L, so there are \(6 - 2 = 4\) choices for the first letter.

Step2: Arrange the remaining letters

After choosing the first letter, we need to arrange the remaining 5 letters. The number of permutations of 5 distinct objects is \(5!\) (which is \(5\times4\times3\times2\times1 = 120\)).

Step3: Calculate the total number of arrangements

Using the multiplication principle, the total number of arrangements is the number of choices for the first letter times the number of permutations of the remaining letters. So, \(4\times5! = 4\times120 = 480\).

Answer:

B. 480