HOW MANY NUMBERS ARE THERE BETWEEN 1 AND 1000
How many numbers are there between 1 and 1000 :
Here we are going to see some practice questions based on the concept fundamental principle of counting.
How many numbers are there between 1 and 1000 - Practice questions
Question 1 :
To travel from a place A to place B, there are two different bus routes B1,B2, two different train routes T1, T2 and one air route A1. From place B to place C there is one bus route say B'1, two different train routes say T'1, T'2 and one air route A'1. Find the number of routes of commuting from place A to place C via place B without using similar mode of transportation.
Solution :
CASE 1 :
If we choose the transportation bus from place A to B, we have to choose either train or air, to go from B to C.
- If we choose B1, we will have 3 ways (T1', T2', A1')
- If we choose B2, we will have 3 ways (T1', T2',A1')
= 3 + 3 = 6 ways
CASE 2 :
If we choose the transportation train from place A to B, we have to choose either bus or air, to go from B to C.
- If we choose T1, we will have 2 ways (B1', A1')
- If we choose T2, we will have 2 ways (B1', A1')
= 2 + 2 = 4 ways
CASE 3 :
If we choose the transportation air from place A to B, we have to choose either bus or train, to go from B to C.
- If we choose A1, we will have 3 ways (B1', T1', T2')
Hence total number of routes = 6 + 4 + 3
= 13 ways
Question 2 :
How many numbers are there between 1 and 1000 (both inclusive) which are divisible neither by 2 nor by 5?
Solution :
We may form one digit, two digit and three digit numbers from 1 to 1000.
One digit numbers not divisible by 2 and 5
The numbers 1, 3, 7 and 9 are not divisible by both 2 and 5.
= 4 numbers
Two digit numbers not divisible by 2 and 5
Since the required numbers are not divisible by bot 2 and 5, it ends with (1, 3, 7, 9)
Unit digit :
We have 4 options
Tens digit :
Other than 0, we have 9 options
= 9 ⋅ 4 = 36 numbers
Three digit numbers not divisible by 2 and 5
Since the required numbers are not divisible by bot 2 and 5, it ends with (1, 3, 7, 9)
Unit digit :
We have 4 options
Hundreds digit :
Other than 0, we have 9 options
Tens digit :
Including 0, we have 10 options
= 10 ⋅ 9 ⋅ 4 = 360 numbers
Hence total number to be formed = 4 + 36 + 360
= 400 numbers
After having gone through the stuff given above, we hope that the students would have understood "How many numbers are there between 1 and 1000 ".
Apart from the stuff given above, if you want to know more about "How many numbers are there between 1 and 1000 ".
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
©All rights reserved. onlinemath4all.com
Recent Articles
-
De Moivre's Theorem and Its Applications
Apr 19, 24 08:30 AM
De Moivre's Theorem and Its Applications -
First Fundamental Theorem of Calculus - Part 1
Apr 17, 24 11:27 PM
First Fundamental Theorem of Calculus - Part 1 -
Polar Form of a Complex Number
Apr 16, 24 09:28 AM
Polar Form of a Complex Number
