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

If $^n{P_5} = 9 \times {^{n - 1}}{P_4}$,then the value of $n$ is

If $4 \times ^{15}P_r = 3 \times ^{16}P_{r-1}$,then $r = \dots$

The number of four-digit even numbers that can be formed using the digits $0, 1, 2,$ and $3$ without repetition is:

The sum of all $4$-digit numbers that can be formed by using the digits $2, 4, 6, 8$ (repetition of digits not allowed) is

All the letters of the word $GTWENTY$ are written in all possible ways with or without meaning and these words are written as in a dictionary. The serial number of the word $GTWENTY$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module