(C) Numbers between $99$ and $1000$ are $3$-digit numbers.We have $6$ digits: ${0, 2, 3, 6, 7, 8}$.Total $3$-digit numbers formed using these $6$ digi

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(C) Numbers between $99$ and $1000$ are $3$-digit numbers.We have $6$ digits: ${0, 2, 3, 6, 7, 8}$.Total $3$-digit numbers formed using these $6$ digits (including those starting with $0$) is $^6P_3 = 6 \times 5 \times 4 = 120$.Numbers starting with $0$ (which are effectively $2$-digit numbers) are formed by choosing $2$ digits from the remaining $5$ digits for the tens and units places: $^5P_2 = 5 \times 4 = 20$.Required numbers $= 120 - 20 = 100$.

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

Medium

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

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

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

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In how many ways can the letters of the word $TRIANGLE$ be arranged such that no two vowels occur together?

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