How many words can be formed by using all the | vedclass

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(C) The word '$TRIVANDRUM$' consists of $10$ letters: $T, R, I, V, A, N, D, R, U, M$.
In this word,the letter '$R$' appears twice,whi

Vedclass · Accepted Answer

$1,814,400$

Vedclass · Answer

(C) The word '$TRIVANDRUM$' consists of $10$ letters: $T, R, I, V, A, N, D, R, U, M$.
In this word,the letter '$R$' appears twice,while all other letters appear once.
The total number of arrangements of $n$ objects where $p$ objects are of one kind and the rest are distinct is given by $\frac{n!}{p!}$.
Here,$n = 10$ and $p = 2$.
Therefore,the number of words that can be formed = $\frac{10!}{2!} = \frac{3,628,800}{2} = 1,814,400$.

How many words can be formed by using all the letters of the word '$TRIVANDRUM$' using each letter exactly once (in $!$)?

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