(A) The letters of the word $MATHS$ are $A, H, M, S, T$. Total letters $= 5$. Words starting with $A$: $4! = 24$. Words starting with $H$: $4! = 24$.

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(A) The letters of the word $MATHS$ are $A, H, M, S, T$. Total letters $= 5$. Words starting with $A$: $4! = 24$. Words starting with $H$: $4! = 24$. Words starting with $M$: $4! = 24$. Words starting with $S$: $4! = 24$. Total words before starting with $T$ is $24 \times 4 = 96$. Now,words starting with $T$: $TA...$: $3! = 6$. $THAMS$: $THA...$: $2! = 2$. $THAM...$: $1! = 1$. $THAMS$: $1$. Serial number $= 96 + 6 + 1 = 103$.

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

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If the letters of the word $MATHS$ are permuted and all possible words so formed are arranged as in a dictionary with serial numbers,then the serial number of the word $THAMS$ is

JEE MAIN 2023 All JEE MAIN

A
$103$
B
$104$
C
$101$
D
$102$

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

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If the letters of the word $MATHS$ are permuted and all possible words so formed are arranged as in a dictionary with serial numbers,then the serial number of the word $THAMS$ is

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