How many even numbers of four digits can be f | vedclass

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

Question

(C) To form a four-digit even number,the units place must be filled by $0, 2, 4,$ or $6$.Case $I$: When $0$ is at the units place.The units place can

Vedclass · Accepted Answer

$420$

Vedclass · Answer

(C) To form a four-digit even number,the units place must be filled by $0, 2, 4,$ or $6$.Case $I$: When $0$ is at the units place.The units place can be filled in $1$ way. The remaining $3$ places can be filled using the remaining $6$ digits $(1, 2, 3, 4, 5, 6)$ in $^6P_3$ ways.Number of ways $= 1 	imes ^6P_3 = \frac{6!}{3!} = 6 	imes 5 	imes 4 = 120$.Case $II$: When $0$ is not at the units place.The units place can be filled by $2, 4,$ or $6$ in $3$ ways. The thousands place cannot be $0$ and cannot be the digit used in the units place,so it can be filled in $5$ ways (out of $6$ remaining digits). The remaining $2$ places can be filled by the remaining $5$ digits in $^5P_2$ ways.Number of ways $= 3 	imes 5 	imes ^5P_2 = 15 	imes \frac{5!}{3!} = 15 	imes 20 = 300$.Total even numbers $= 120 + 300 = 420$.

How many even numbers of four digits can be formed with the digits $0, 1, 2, 3, 4, 5$ and $6$,if no digit is used more than once?

Similar Questions

$12$ persons are to be arranged at a round table. If two particular persons among them are not to be side by side,the total number of arrangements is

There are $m$ men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by $84,$ then the value of $m$ is

The number of four-digit numbers that can be formed using the digits $1, 2, 3, 4,$ and $5$ in which at least two digits are identical is

There are $5$ letters and $5$ directed envelopes. Find the number of ways in which the letters can be put into the envelopes so that all are not put in directed envelopes?

Vedclass Test Series

Exam Paper Generator

Online Exam Module