Total number of 6-digit numbers in which only | vedclass

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

Question

(A) To form a $6$-digit number using the digits ${1, 3, 5, 7, 9}$,one digit must be repeated exactly twice,and the other four digits must appear exact

Vedclass · Accepted Answer

$\frac{5}{2}(6!)$

Vedclass · Answer

(A) To form a $6$-digit number using the digits ${1, 3, 5, 7, 9}$,one digit must be repeated exactly twice,and the other four digits must appear exactly once.Step $1$: Select the digit to be repeated. There are $5$ choices $(^{5}C_{1})$.Step $2$: Arrange these $6$ digits (where one digit is repeated twice). The number of arrangements is given by $\frac{6!}{2!}$.Step $3$: The total number of such $6$-digit numbers is $^{5}C_{1} 	imes \frac{6!}{2!} = 5 	imes \frac{720}{2} = 5 	imes 360 = 1800$.Note: $\frac{6!}{2!} = 360$,so $5 	imes 360 = 1800$. Comparing with the options,$\frac{5}{2}(6!) = 5 	imes 360 = 1800$.

Total number of $6$-digit numbers in which only and all the five digits $1, 3, 5, 7,$ and $9$ appear,is

Similar Questions

Find how many words can be formed out of the letters of the word '$ORIENTAL$' so that vowels always occupy the odd places.

The number of ways in which four letters of the word '$MATHEMATICS$' can be arranged is given by

If the four-letter words (need not be meaningful) are to be formed using the letters from the word "$MEDITERRANEAN$" such that the first letter is $R$ and the fourth letter is $E,$ then the total number of all such words is

The number of rectangles that can be obtained by joining four of $12$ vertices of a $12$-sided regular polygon is:

$A$ number lock consists of three rings. If the $1^{st}$ ring is marked with digits $0$ to $9$,the $2^{nd}$ ring is marked with prime numbers greater than $2$ but less than $30$,and the $3^{rd}$ ring is marked with all vowels,find the total number of unsuccessful attempts.

Vedclass Test Series

Exam Paper Generator

Online Exam Module