harDill wrote:

Bunuel wrote:

Official Solution:

In how many ways can the letters of the word LEVEL be arranged so that the first letter is \(L\) and the last letter is \(E\)?

A. 4

B. 6

C. 10

D. 12

E. 24

We need all possible arrangements which fit the following form: \(L---E\). Three distinct letters left (\(V\), \(E\) and \(L\)) can be arranged in three slots between \(L\) and \(E\) in \(3!=6\) ways.

Answer: B

bunuel,

why are we not dividing it by 2!*2! ( reason- L and E are repeated)

Because we are told that the first letter (L) and the last letter (E) are fixed. Only the three letters (V, E and L) between them can be arranged.

How do we know not to count the arrangements of the alternate L and alternate E in the end spots? Is there verbiage that would have indicated otherwise if they did not count as the same? i.e.