How many 5 digit telephone numbers can be con | vedclass

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

Question

(A) $5$ digit telephone number starts with $67$. Since the first two digits are fixed as $6$ and $7$,we need to fill the remaining $3$ positions. The

Vedclass · Accepted Answer

$336$

Vedclass · Answer

(A) $5$ digit telephone number starts with $67$. Since the first two digits are fixed as $6$ and $7$,we need to fill the remaining $3$ positions. The available digits are ${0, 1, 2, 3, 4, 5, 8, 9}$,which are $8$ distinct digits. Since no digit can be repeated,we need to arrange $3$ digits out of these $8$ available digits. The number of ways to arrange $3$ digits out of $8$ is given by the permutation formula $^nP_r = \frac{n!}{(n-r)!}$. Here,$n = 8$ and $r = 3$. $^8P_3 = \frac{8!}{(8-3)!} = \frac{8!}{5!} = 8 	imes 7 	imes 6 = 336$.

How many $5$ digit telephone numbers can be constructed using the digits $0$ to $9$,if each number starts with $67$ and no digit appears more than once?

Similar Questions

How many numbers between $3000$ and $4000$ can be formed using the digits $3, 4, 5, 6, 7, 8$ without repetition,such that the numbers are divisible by $5$?

There are $3$ candidates for a post and one is to be selected by the votes of $7$ men. The number of ways in which votes can be given is

How many words can be formed using the letters of the word $INSURANCE$,such that all vowels always come together?

Evaluate $4! - 3!$

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 $P$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module