How many 3-digit odd numbers can be formed fr | vedclass

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(A) $(i)$ When repetition of digits is not allowed: Since we have to form a $3$-digit odd number,the digit at the unit's place must be odd. The unit's

Vedclass · Accepted Answer

$(i)$ $60,$ (ii) $108$

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(A) $(i)$ When repetition of digits is not allowed: Since we have to form a $3$-digit odd number,the digit at the unit's place must be odd. The unit's place can be filled by $1, 3,$ or $5,$ which is $3$ ways.Now,the ten's place can be filled by any of the remaining $5$ digits in $5$ ways,and the hundred's place can be filled by the remaining $4$ digits in $4$ ways.Therefore,the total number of $3$-digit odd numbers $= 3 	imes 5 	imes 4 = 60$.(ii) When repetition of digits is allowed: The unit's place can be filled by $1, 3,$ or $5,$ which is $3$ ways. Since repetition is allowed,the ten's place can be filled by any of the $6$ digits in $6$ ways,and the hundred's place can also be filled by any of the $6$ digits in $6$ ways.Therefore,the total number of $3$-digit odd numbers $= 3 	imes 6 	imes 6 = 108$.

How many $3$-digit odd numbers can be formed from the digits $1, 2, 3, 4, 5, 6$ when
$(i)$ repetition of digits is not allowed
(ii) repetition of digits is allowed?

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How many $3$-digit odd numbers can be formed from the digits $1, 2, 3, 4, 5, 6$ when$(i)$ repetition of digits is not allowed(ii) repetition of digits is allowed?