(A) Numbers lying between $99$ and $1000$ are $3$-digit numbers.We have $6$ available digits: $\{0, 2, 3, 6, 7, 8\}$.For a $3$-digit number,the hundre

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(A) Numbers lying between $99$ and $1000$ are $3$-digit numbers.We have $6$ available digits: $\{0, 2, 3, 6, 7, 8\}$.For a $3$-digit number,the hundreds place cannot be $0$.Therefore,the hundreds place can be filled by any of the $5$ digits: $\{2, 3, 6, 7, 8\}$ ($5$ ways).The tens place can be filled by any of the remaining $5$ digits (including $0$) ($5$ ways).The units place can be filled by any of the remaining $4$ digits ($4$ ways).Total numbers = $5 \times 5 \times 4 = 100$.

Class 11 Mathematics Permutations and Combinations Definition of permutation, Number of permutations with or without repetition, Conditional permutations

Easy

How many numbers lying between $99$ and $1000$ can be formed using the digits $2, 3, 7, 0, 8, 6$ if each digit is used only once in each number?

A
$100$
B
$90$
C
$120$
D
$80$

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Permutations and Combinations

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

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MediumMHT CET 2023

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How many permutations can be formed from the letters of the word $ALGEBRA$ without changing the relative positions of the vowels and consonants?

Easy

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How many words can be formed using the letters of the word $MAXIMUM$ such that no two vowels are together?

Medium

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The number of $4$-letter words, with or without meaning, which can be formed using the letters of '$PQRPQRSTUVP$',is:

DifficultJEE MAIN 2026

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If all the words (with or without meaning) having five letters,formed using the letters of the word $SMALL$ and arranged as in a dictionary,then the position of the word $SMALL$ is:

DifficultJEE MAIN 2016

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How many numbers lying between $99$ and $1000$ can be formed using the digits $2, 3, 7, 0, 8, 6$ if each digit is used only once in each number?

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The teacher wants to arrange $5$ students on the platform such that the boy $B_1$ occupies the second position and the girls $G_1$ and $G_2$ are always adjacent to each other. Then,the number of such arrangements is

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