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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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:

Similar Questions

If $^n{P_5} = 9 \times {^{n - 1}}{P_4}$,then the value of $n$ is

The number of arrangements that can be formed from the letters $a, b, c, d, e, f$ taken $3$ at a time without repetition,such that each arrangement contains at least one vowel,is

How many $6$-digit numbers can be formed using the digits of the number $112233$?

The number of arrangements of the letters of the word $ARRANGEMENT$ in which two $E$s do not occur adjacently is

If the letters of the word $RACHIT$ are arranged in all possible ways and these words are listed in dictionary order,what is the rank of the word $RACHIT$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module