(A) The word $EQUATION$ consists of $8$ distinct letters: $E, Q, U, A, T, I, O, N$.Since all letters are distinct,the number of ways to arrange these

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(A) The word $EQUATION$ consists of $8$ distinct letters: $E, Q, U, A, T, I, O, N$.Since all letters are distinct,the number of ways to arrange these $8$ letters taken all at a time is given by the permutation formula $n!$,where $n = 8$.Therefore,the total number of words that can be formed is $8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 40320$.

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

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How many words,with or without meaning,can be formed using all the letters of the word $EQUATION$,using each letter exactly once?

A
$40320$
B
$5040$
C
$20160$
D
$80640$

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Permutation and Combination

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

Let $P$ be the set of seven-digit numbers with the sum of their digits equal to $11$. If the numbers in $P$ are formed by using the digits $1, 2,$ and $3$ only,then the number of elements in the set $P$ is:

DifficultJEE MAIN 2025

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If four-letter words (need not be meaningful) are to be formed using the letters from the word $MEDITERRANEAN$ such that the first letter is $R$ and the fourth letter is $E$,then the total number of such words is

DifficultJEE MAIN 2016

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If $^nP_4 : ^nP_5 = 1 : 2$,then $n = \dots$

Easy

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What is the rank of the word "$MOTHER$" when all possible words are formed using all its letters and arranged as in a dictionary?

EasyAP EAMCET 2022

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If $7 \cdot ^nP_3 = 20 \cdot ^{n+1}P_2$,then $n = \dots$

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How many words,with or without meaning,can be formed using all the letters of the word $EQUATION$,using each letter exactly once?

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Let $P$ be the set of seven-digit numbers with the sum of their digits equal to $11$. If the numbers in $P$ are formed by using the digits $1, 2,$ and $3$ only,then the number of elements in the set $P$ is:

If four-letter words (need not be meaningful) are to be formed using the letters from the word $MEDITERRANEAN$ such that the first letter is $R$ and the fourth letter is $E$,then the total number of such words is

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