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

If $C(n, 7) = C(n, 5)$,find $n$.

The number of ways in which we can select three numbers from $1$ to $30$ so as to exclude every selection of all even numbers is

The exponent of $3$ in $100!$ is

$P_1$ and $P_2$ are two distinct and intersecting planes. Three non-collinear points lie on $P_1$ and another three non-collinear points lie on $P_2$ (none being on the line of intersection of the planes). Then,the maximum number of tetrahedrons formed using these six points is:

Six objects $O_1$ to $O_6$ are arranged one on top of the other. In how many ways can these be arranged such that $O_1$ and $O_2$ are the $2$ bottom-most objects?

Vedclass Test Series

Exam Paper Generator

Online Exam Module