Question

number of words formed using the word BANANA in which no two "N's" are together ( Permutations and Combination)​

Answer 1

       

First, we have to find the total no. of words formed by the letters in the words BANANA.

BANANA is a 6 letter word, with 1 'B', 2 'N's and 3 'A's.

So the total no. of words is,

$\boxed{\frac{6!}{1! \times 2! \times 3!}=\frac{720}{12}=60}$

So we can make 60 words in total.

Now we have to deduct the no. of words in which the two 'N's are together, from this 60.

So let's find the no. of words in which 2 'N's are together.

Let the two 'N's be a one letter, so let me indicate it as X.

Consider a word BAAAX, which is actually BAAANN, in which the two 'N's are together.

BAAAX is a 5 letter word, with 1 'B' and 3 'A's.

So the no. of words in which the two 'N's are together is,

$\boxed{\frac{5!}{1! \times 3!}=\frac{120}{6}=20}$

Now deduct this 20 from the no. of total words, i.e., 60. So we get,

60 - 20 = 40

So there are 40 words in which none of the two 'N's are together.

Hope this helps. Plz ask me if you've any doubt on my answer.

Thank you. :-))

$\mathfrak{\#adithyasajeevan}$