(A) The word $BANANA$ consists of $6$ letters in total,where $A$ appears $3$ times,$N$ appears $2$ times,and $B$ appears $1$ time.The number of permut

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(A) The word $BANANA$ consists of $6$ letters in total,where $A$ appears $3$ times,$N$ appears $2$ times,and $B$ appears $1$ time.The number of permutations of $n$ objects where $p$ are of one kind,$q$ are of another kind,and $r$ are of a third kind is given by $\frac{n!}{p!q!r!}$.Here,$n = 6$,$p = 3$ (for $A$),and $q = 2$ (for $N$).Total number of permutations $= \frac{6!}{3! \times 2!} = \frac{720}{6 \times 2} = \frac{720}{12} = 60$.

Class 11 Mathematics Permutation and Combination Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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What is the total number of permutations of the letters of the word $BANANA$?

A
$60$
B
$120$
C
$720$
D
$24$

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Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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What is the total number of permutations of the letters of the word $BANANA$?

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