(A) To form a $3$-digit number using the digits $1, 2, 3, 4,$ and $5$ without repetition,we need to fill $3$ places (hundreds,tens,and units).The hund

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(A) To form a $3$-digit number using the digits $1, 2, 3, 4,$ and $5$ without repetition,we need to fill $3$ places (hundreds,tens,and units).The hundreds place can be filled in $5$ ways (using any of the digits $1, 2, 3, 4, 5$).Since repetition is not allowed,the tens place can be filled in $4$ remaining ways.The units place can then be filled in $3$ remaining ways.By the multiplication principle,the total number of $3$-digit numbers is $5 \times 4 \times 3 = 60$.

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

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How many $3$-digit numbers can be formed from the digits $1, 2, 3, 4,$ and $5$ assuming that repetition of the digits is not allowed?

A
$60$
B
$120$
C
$20$
D
$10$

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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 $3$-digit numbers can be formed from the digits $1, 2, 3, 4,$ and $5$ assuming that repetition of the digits is not allowed?

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