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(D) To form a four-digit odd number using the digits ${0, 1, 2, 3, 5, 7}$ with repetition allowed:$1$. The last digit (units place) must be odd to mak

Vedclass · Accepted Answer

$720$

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(D) To form a four-digit odd number using the digits ${0, 1, 2, 3, 5, 7}$ with repetition allowed:$1$. The last digit (units place) must be odd to make the number odd. The available odd digits are ${1, 3, 5, 7}$. Thus,the units place can be filled in $4$ ways.$2$. The first digit (thousands place) cannot be $0$ because the number must be a four-digit number. The available digits for this place are ${1, 2, 3, 5, 7}$. Thus,the thousands place can be filled in $5$ ways.$3$. The second digit (hundreds place) can be any of the $6$ digits ${0, 1, 2, 3, 5, 7}$. Thus,it can be filled in $6$ ways.$4$. The third digit (tens place) can be any of the $6$ digits ${0, 1, 2, 3, 5, 7}$. Thus,it can be filled in $6$ ways.Using the fundamental principle of counting,the total number of such four-digit 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 allowed) are

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