How many numbers lying between 99 and 1000 ca | vedclass

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

Question

(A) The numbers lying between $99$ and $1000$ are all $3$-digit numbers.We have $6$ digits available: ${0, 2, 3, 6, 7, 8}$.$A$ $3$-digit number cannot

Vedclass · Accepted Answer

$100$

Vedclass · Answer

(A) The numbers lying between $99$ and $1000$ are all $3$-digit numbers.We have $6$ digits available: ${0, 2, 3, 6, 7, 8}$.$A$ $3$-digit number cannot have $0$ at the hundreds place.Total ways to arrange $3$ digits out of $6$ is given by $^6P_3 = 6 	imes 5 	imes 4 = 120$.However,we must exclude the cases where $0$ is at the hundreds place. If $0$ is fixed at the hundreds place,we need to arrange $2$ more digits from the remaining $5$ digits in the tens and units places. This is given by $^5P_2 = 5 	imes 4 = 20$.Therefore,the total number of valid $3$-digit numbers is $120 - 20 = 100$.

How many numbers lying between $99$ and $1000$ can be formed using the digits $2, 3, 7, 0, 8, 6$,if each digit can be used only once in each number?

Similar Questions

$A$ father with $8$ children takes them $3$ at a time to the Zoological gardens,as often as he can without taking the same $3$ children together more than once. The number of times each child will go to the garden is

The number of circular permutations of $n$ different objects is

The number of numbers between $2,000$ and $5,000$ that can be formed using the digits $0, 1, 2, 3, 4$ (repetition of digits is not allowed) which are multiples of $3$ is?

Out of $5$ apples,$10$ mangoes,and $15$ oranges,$15$ fruits are to be distributed between two persons. Find the total number of ways of distribution.

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module