(A) Numbers less than $1000$ can be $1$-digit,$2$-digit,or $3$-digit numbers.Number of $1$-digit numbers $= ^6P_1 = 6$.Number of $2$-digit numbers $=

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(A) Numbers less than $1000$ can be $1$-digit,$2$-digit,or $3$-digit numbers.Number of $1$-digit numbers $= ^6P_1 = 6$.Number of $2$-digit numbers $= ^6P_2 = 6 \times 5 = 30$.Number of $3$-digit numbers $= ^6P_3 = 6 \times 5 \times 4 = 120$.Total numbers $= 6 + 30 + 120 = 156$.

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

Medium

How many numbers less than $1000$ can be formed using the digits $1, 2, 3, 4, 5, 6$ if repetition is not allowed?

A
$156$
B
$160$
C
$150$
D
None of these

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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 less than $1000$ can be formed using the digits $1, 2, 3, 4, 5, 6$ if repetition is not allowed?

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