The number of six-digit natural numbers that | vedclass

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

Question

(D) We need to form a six-digit number using the digits $\{0, 2, 3, 4, 5, 6, 7, 8\}$.There are $8$ available digits in total.For a six-digit number,th

Vedclass · Accepted Answer

$7 	imes 2^{15}$

Vedclass · Answer

(D) We need to form a six-digit number using the digits $\{0, 2, 3, 4, 5, 6, 7, 8\}$.There are $8$ available digits in total.For a six-digit number,the first digit (at the hundred-thousands place) cannot be $0$. Thus,there are $7$ choices for the first digit $(\{2, 3, 4, 5, 6, 7, 8\})$.Since repetition of digits is allowed,each of the remaining $5$ positions can be filled by any of the $8$ available digits.Therefore,the total number of six-digit numbers is:$7 	imes 8 	imes 8 	imes 8 	imes 8 	imes 8 = 7 	imes 8^5$Since $8 = 2^3$,we have $8^5 = (2^3)^5 = 2^{15}$.Thus,the total number of such six-digit numbers is $7 	imes 2^{15}$.

The number of six-digit natural numbers that can be formed using the digits $2, 3, 4, 0, 5, 6, 7, 8$ (repetition of digits is allowed) is:

Similar Questions

${ }^{20}P_5 - { }^{19}P_5 = $

How many $5$-digit numbers can be formed using the digits $1, 2, 3, 4, 5$ such that the number is divisible by $4$?

$(n - r + 1) \times ^nP_{r - 1} = \dots$

The number of arrangements of the letters of the word $SATAYPAUL$ such that no two $A$ are together and the middle letter is a consonant,is

The number of integers greater than a million that can be formed using the digits $2, 3, 0, 3, 4, 2, 3$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module