How many 6-digit numbers can be formed using | vedclass

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

Question

(A) The available odd digits are $\{1, 3, 5, 7, 9\}$. There are $5$ such digits.To form a $6$-digit number using only these $5$ digits such that all d

Vedclass · Accepted Answer

$5 	imes \frac{6!}{2!}$

Vedclass · Answer

(A) The available odd digits are $\{1, 3, 5, 7, 9\}$. There are $5$ such digits.To form a $6$-digit number using only these $5$ digits such that all digits appear at least once,exactly one digit must be repeated.Step $1$: Select the digit to be repeated from the $5$ available odd digits in $^5C_1 = 5$ ways.Step $2$: Arrange these $6$ digits (where one digit is repeated twice) in $\frac{6!}{2!}$ ways.Total numbers = $5 	imes \frac{6!}{2!} = 5 	imes \frac{720}{2} = 5 	imes 360 = 1800$.

How many $6$-digit numbers can be formed using only odd digits,such that all odd digits appear at least once?

Similar Questions

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

If four-digit numbers are formed by using the digits $1, 2, 3, 4, 5, 6, 7$ without repetition,then how many of these numbers are exactly divisible by $25$?

How many words can be formed using the letters of the word '$ARTICLE$' if the vowels always occupy odd positions?

$A$ car will hold $2$ persons in the front seat and $1$ person in the rear seat. If among $6$ persons $2$ can drive,then the number of ways in which the car can be filled is

$n$-digit numbers are formed using only three digits $2, 5,$ and $7$. The smallest value of $n$ for which $900$ such distinct numbers can be formed is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module