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

select the correct answer.\nconsider 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.\nconsider 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 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