(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

Medium

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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Permutation and Combination

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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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How many words of $7$ letters can be formed by selecting $4$ consonants and $3$ vowels from $6$ consonants and $5$ vowels?

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