How many 3-digit even numbers can be formed u | vedclass

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

Question

(C) To form a $3$-digit even number,the units place must be filled with an even digit from the set $\{1, 2, 3, 4, 6, 7\}$.The available even digits ar

Vedclass · Accepted Answer

$60$

Vedclass · Answer

(C) To form a $3$-digit even number,the units place must be filled with an even digit from the set $\{1, 2, 3, 4, 6, 7\}$.The available even digits are $2, 4,$ and $6$. Thus,the units place can be filled in $3$ ways.Since digits cannot be repeated,after filling the units place,we have $5$ digits remaining to fill the hundreds and tens places.The number of ways to fill the hundreds and tens places using the remaining $5$ digits is given by the permutation formula $^5P_2$.$^5P_2 = \frac{5!}{(5-2)!} = \frac{5 	imes 4 	imes 3!}{3!} = 5 	imes 4 = 20$.By the multiplication principle,the total number of $3$-digit even numbers is $3 	imes 20 = 60$.

How many $3$-digit even numbers can be formed using the digits $1, 2, 3, 4, 6, 7$,if no digit is repeated?

Similar Questions

The number of ways in which $n$ distinct objects can be put into two different boxes is

In a class of $20$ students,in how many ways can the following prizes be awarded?
If the first and second prizes are for Mathematics,the first and second prizes for Physics,the first prize for Chemistry,and the first prize for English are to be awarded.

The number of integers greater than $3000$ that can be formed by using any number of digits from the set $\{0, 1, 2, 3, 4, 5\}$ without repetition is:

The number of words that can be written using all the letters of the word "$IRRATIONAL$" is

The number of integers greater than a million that can be formed using the digits $2, 3, 0, 3, 4, 2, 3$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module