How many odd numbers of four digits can be fo | vedclass

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Question

(A) four-digit number is odd if its unit place is occupied by an odd digit. The available odd digits from the set ${0, 1, 2, 3, 4, 7, 8}$ are ${1, 3,

Vedclass · Accepted Answer

$150$

Vedclass · Answer

(A) four-digit number is odd if its unit place is occupied by an odd digit. The available odd digits from the set ${0, 1, 2, 3, 4, 7, 8}$ are ${1, 3, 7}$.$1$. The unit place can be filled by any of the $3$ odd digits in $^3P_1 = 3$ ways.$2$. The thousandth place cannot be $0$. Since one odd digit is already used in the unit place,there are $6 - 1 = 5$ remaining digits available for the thousandth place (excluding $0$ and the digit used in the unit place). Thus,it can be filled in $5$ ways.$3$. The remaining two places (hundredth and tenth) can be filled by the remaining $5$ digits in $^5P_2 = 5 	imes 4 = 20$ ways.Therefore,the total number of four-digit odd numbers is $3 	imes 5 	imes 20 = 300$.

How many odd numbers of four digits can be formed with the digits $0, 1, 2, 3, 4, 7$ and $8$?

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