How many 3-digit numbers can be formed using | vedclass

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

Question

(B) $3$-digit number consists of three places: Hundreds,Tens,and Units.For the Hundreds place,the digit '$0$' cannot be used because a $3$-digit numbe

Vedclass · Accepted Answer

$100$

Vedclass · Answer

(B) $3$-digit number consists of three places: Hundreds,Tens,and Units.For the Hundreds place,the digit '$0$' cannot be used because a $3$-digit number cannot start with $0$. Thus,we can choose from ${1, 3, 5, 7}$,which gives $4$ options.For the Tens place,since repetition is allowed,all $5$ digits ${0, 1, 3, 5, 7}$ can be used,giving $5$ options.For the Units place,since repetition is allowed,all $5$ digits ${0, 1, 3, 5, 7}$ can be used,giving $5$ options.Therefore,the total number of $3$-digit numbers $= 4 	imes 5 	imes 5 = 100$.

How many $3$-digit numbers can be formed using $0, 1, 3, 5, 7$ when repetition is allowed?

Similar Questions

How many numbers can be formed with the digits $1, 2, 3, 4, 3, 2, 1$ so that odd digits always occupy the odd places?

In a circus, there are $10$ cages to accommodate $10$ animals. Out of these, $4$ cages are so small that $5$ specific animals cannot enter them. In how many ways is it possible to accommodate the $10$ animals in these $10$ cages?

If $12 \cdot {}^{n}C_{2} = {}^{2n}C_{3}$,find $n$.

In how many different ways can the letters of the word $MATHEMATICS$ be arranged?

How many $3$-digit numbers are there with no digit repeated?

Vedclass Test Series

Exam Paper Generator

Online Exam Module