Question

the five letters of the word NEVER are arranged in random order in a straight line

how many different orders of the letters are possible?!

Answer 1

5 possibilities for first letters.
4 for second.
3 for third.
2 for fourth.
1 for fifth.

It'd be \(5!\), but then comes a great confusion. THERE ARE TWO E's. Easy. You must see the number of ways to arrange two E's and divide them and i.e., 2!

\(\Large \color{MidnightBlue}{\Rightarrow {5! \over 2!} }\)

Answer 2

Final answer is 5 * 4 * 3 = 20 * 3 = 60

Answer 3

okay so this question is asking for permutations, i understand that, but i do not understand why i have to divide by 2! when it is just arrangements of 5 letters... if that never had two E's i would just do 5! so why not now?
i thought i would only divide by 2! if it was a combination? so confused

Answer 4

Haha, see. If we name them E1 and E2, and for example, we have this:

R E1 E2 V R
R E2 E1 V R

Well, this makes no difference right? If it mattered about the order of E1 and E2, then it'd be 5! only.

Answer 5

thank you! life saver :P

Answer 6

Haha, another user called me a lifesaver on here today

Answer 7

you literally are... if i faily my math exam tomorrow there is no hope, so the more you clear things up for me the more of my life you save ;D

Answer 8

Haha best of luck