Assuming that no two consecutive digits are s | vedclass

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

Question

(A) For an $n$-digit number,the first digit (at the leftmost position) can be any digit from $1$ to $9$ (since it cannot be $0$). So,there are $9$ cho

Vedclass · Accepted Answer

$9 	imes 9^{n-1}$

Vedclass · Answer

(A) For an $n$-digit number,the first digit (at the leftmost position) can be any digit from $1$ to $9$ (since it cannot be $0$). So,there are $9$ choices for the first digit.For the second digit,it can be any digit from $0$ to $9$ except the one used for the first digit. So,there are $9$ choices.For the third digit,it can be any digit from $0$ to $9$ except the one used for the second digit. So,there are $9$ choices.Continuing this pattern,for each of the remaining $(n-1)$ positions,there are $9$ choices.Therefore,the total number of $n$-digit numbers is $9 	imes 9 	imes 9 	imes \dots 	imes 9$ ($(n-1)$ times) $= 9 	imes 9^{n-1}$.

Assuming that no two consecutive digits are same,the number of $n$-digit numbers is:

Similar Questions

There are $10$ distinct letters of the English alphabet. Words of $5$ letters are formed using these letters. How many such words can be formed if at least one letter is repeated?

The value of ${}^7P_3 - 3({}^6P_2)$ is equal to

How many $5$-digit numbers can be formed using the digits $1$ and $2$,such that exactly one digit is different from the others?

How many $3$-digit odd numbers can be formed using the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ if repetition of digits is not allowed?

The total number of words (with or without meaning) that can be formed out of the letters of the word $'DISTRIBUTION'$ taken four at a time,is equal to...............

Vedclass Test Series

Exam Paper Generator

Online Exam Module