Question

Using the alphabets of the word ' BANANA' determine how many words can be formed so
that the two N's are not together. (use permutation /combination)

Answer 1

Hi, is it OK if I walk you through the question, or are you just looking for the answer?

Answer 2

i.e. I can help you step by step, or just give you the answer.

Answer 3

Which do you prefer?

Answer 4

steps

Answer 5

OK. First of all, is it Permutations, or is it Combinations?

Answer 6

"I don't know" is OK, you know, just say something :D

Answer 7

permutation

Answer 8

Great! Suppose there wasn't the condition about the two Ns, how many permutations would be possible?

Answer 9

60 ?

Answer 10

Great! Now, try working out the number of permutations where the 2 N's ARE together.

Answer 11

40?

Answer 12

How did you work that out?

Answer 13

(5!/3!)*2 ?

Answer 14

OK, and where did the 5!, the 3! and the *2, each come from?

Answer 15

i don't know

Answer 16

Don't worry, I'm not suggesting that anything is right/wrong, I just need you to explain your steps to me.

Answer 17

If you really don't know, I can do this step for you. Would you like that?

Answer 18

Are you still there JOYAL? (But if you need more time, just say so!)

Answer 19

steps.....

Answer 20

OK. You knew how to work out the 60, earlier on. Now we want to find the permutations if the two N's ARE together. My favourite way of doing this is to imagine them glued together, so they make something a bit like 1 letter M, instead of two letter N's. If you have the letters BAMAA, how many permutations are there?

Answer 21

@BasketWeave 20 ?

Answer 22

Well done! So if there's 60 ways in total of arranging the letters, and 20 of them DO have the two N's together, how many DON'T have the N's together?

Answer 23

@Joyal Was this question confusing?

Answer 24

40

Answer 25

Well done! That's the answer to your original question. Did that all make sense?