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How many distinguishable permutations of the letters in the word of BANANA are there?

1. $720$
2. $120$
3. $60$
4. $360$

Number of permutation of n objects with n1 identical objects of type 1, n2 identical objects of type 2, ......and nk identical objects of type k is $\frac{n!}{n_{1}!n_{2}!....n_{k}!}$

Permutation of letter BANANA are $\frac{6!}{3!2!}= 60$

Option c) is correct

$\text{Total number of letters in ''BANANA''} = 6$

$\text{Total number of 'A' in the word ''BANANA'' }= 3$

$\text{ Total number of 'N' in the word ''BANANA''}= 2$

$\text{Total distinguishable permutations of the letters ''BANANA'' }=\frac{6!}{3! 2!}=60$

$\text{For text in latex you may use \text{} option.}$ Also for begin quote  can be used which will render as $$.
Thank you..:)
Distinguishable permutation means the letters won't be repeated. Here BANANA contains 6 letters in which N has been repeated twice and A has been repeated thrice. Hence number of distinguishable permutations = 6!/(3!2!) = 60
(6!)/ (1!).(2!).(3!) =  (720)/ 1.2.6 = 60

so option C

1 vote