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

Find the number of arrangements of the letters of the word $INDEPENDENCE$. In how many of these arrangements do the words begin with $I$ and end in $P$?

All the letters of the word $EAMCET$ are arranged in all possible ways. The number of such arrangements in which two vowels are not adjacent to each other is

How many numbers can be formed using the digits $1, 2, 3, 4$ if repetition of digits is not allowed?

If $^nP_4 : ^nP_5 = 1 : 2$,then $n = \dots$

The letters of the word "$UDAYPUR$" are written in all possible ways with or without meaning and these words are arranged as in a dictionary. The rank of the word "$UDAYPUR$" is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module