Total number of four-digit odd numbers that c | vedclass

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(D) four-digit number is represented as $d_1 d_2 d_3 d_4$.For the number to be odd,the last digit $d_4$ must be chosen from the set $\{1, 3, 5, 7\}$.

Vedclass · Accepted Answer

$720$

Vedclass · Answer

(D) four-digit number is represented as $d_1 d_2 d_3 d_4$.For the number to be odd,the last digit $d_4$ must be chosen from the set $\{1, 3, 5, 7\}$. There are $4$ ways to fill $d_4$.For the first digit $d_1$,it cannot be $0$ (otherwise it would be a three-digit number). Thus,$d_1$ can be chosen from $\{1, 2, 3, 5, 7\}$,which gives $5$ ways.For the second digit $d_2$ and third digit $d_3$,since repetition is allowed,each can be filled by any of the $6$ digits $\{0, 1, 2, 3, 5, 7\}$. Thus,there are $6$ ways for $d_2$ and $6$ ways for $d_3$.Using the fundamental principle of counting,the total number of such odd numbers is $5 	imes 6 	imes 6 	imes 4 = 720$.

Total number of four-digit odd numbers that can be formed using $0, 1, 2, 3, 5, 7$ (repetition is allowed) is:

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