(B) To form a $3$ digit odd number,the unit's place (extreme right) must be filled by an odd digit from the set $\{1, 2, 3, 4, 5, 6\}$.The odd digits

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(B) To form a $3$ digit odd number,the unit's place (extreme right) must be filled by an odd digit from the set $\{1, 2, 3, 4, 5, 6\}$.The odd digits available are $\{1, 3, 5\}$,so there are $3$ ways to fill the unit's place.Since repetition is allowed,the hundreds place (extreme left) can be filled by any of the $6$ digits in $6$ ways.The tens place (middle) can also be filled by any of the $6$ digits in $6$ ways.Therefore,the total number of such odd numbers is $6 \times 6 \times 3 = 108$.

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

Easy

The number of $3$ digit odd numbers that can be formed by using the digits $1, 2, 3, 4, 5, 6$ when the repetition of digits is allowed is:

A
$60$
B
$108$
C
$36$
D
$30$

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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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The number of $3$ digit odd numbers that can be formed by using the digits $1, 2, 3, 4, 5, 6$ when the repetition of digits is allowed is:

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