How many seven letter words can be formed using the letters of the word "BENZENE"?

Question

How many seven letter words can be formed using the letters of the word "BENZENE"?

Answer 1

7!/(3!)(2!) the 7 for the 7 letters in Benzene, the 3 for the 3 E's, and the 2 for the 2 N's.

So, 5040/(6*2)= 420, that is 420 words where most won't make any sense in English of course.

Don't listen to those other guys. Benzene and OBVIOUSLY Zen are 2 words you can make. HAHA.

Answer 2

Assumption: By words you mean arrangements including "nonsensical" words Otherwise there is only one 7-letter word and that is BENZENE

Solution:

If the letters were all different then 7!

But there are 2 N's and 3 E's
so number of different words = 7!/(2! x 3!) = 420

This is because the different ways of arranging the N's and the E's will not make different words

eg BE(1)N(1)ZE(2)N(2)E(3) is the same as
BE(1)N(1)ZE(3)N(2)E(2)
BE(2)N(1)ZE(1)N(2)E(3)
BE(2)N(1)ZE(3)N(2)E(1)
BE(3)N(1)ZE(1)N(2)E(2)
BE(3)N(1)ZE(2)N(2)E(1)
BE(1)N(1)ZE(2)N(2)E(3)
BE(1)N(2)ZE(3)N(1)E(2)
BE(2)N(2)ZE(1)N(1)E(3)
BE(2)N(2)ZE(3)N(1)E(1)
BE(3)N(2)ZE(1)N(1)E(2)
BE(3)N(2)ZE(2)N(1)E(1)

Where E(1), E(2), E(3), N(1), N(2) are my feeble attempt to differentiate the different E's and N's. The real world does not do so so all the words look exactly the same and so these have to be removed from the count.

And you can do this with any different arrangement of BENZENE so the different arrangements appear 2! times for the repeated N's and 3! times for the repeated E's

Answer 3

That's the mississippi problem again. 7! / (3!x2!).
There are 7 ways to arrange 7 letters, divide out the arrangements of 3 identical letters (E) and 2 identical letters (N)

Answer 4

Benzene is the only one...
according to magswordfinder.com

Answer 5

Only 1 Benzene.

Good Luck!

Answer 6

7!/2=5040/2=2520
divide by 2 because the 2 "E"'s are interchangeable