select the correct answer. consider the word pencil. if all of the letters are used, and the first letter…

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?\na. 720\nb. 480\nc. 360\nd. 96

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?\na. 720\nb. 480\nc. 360\nd. 96

Answer

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 possibilities for the first letter.

Step2: Determine arrangements of remaining letters

After choosing the first letter, there are 5 remaining letters. The number of ways to arrange these 5 remaining letters is given by the permutation formula (n!=\ n\times(n - 1)\times\cdots\times1), so the number of arrangements of 5 letters is (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 the product of the number of possibilities for the first letter and the number of arrangements of the remaining 5 letters. So the total number of arrangements is (4\times5!=4\times120 = 480).

Answer:

B. 480