Advertisements
Advertisements
प्रश्न
How many numbers are there between 1 and 1000 (both inclusive) which are divisible neither by 2 nor by 5?
Advertisements
उत्तर
From 1 to 1000, the numbers ÷ by 2 = 500
The number ÷ by 5 = 200
And the numbers ÷ by 10 = 100(5 × 2 = 10)
So number ÷ by 2 or 5 = 500 + 200 – 100 = 600
Total numbers from 1 to 1000 = 1000
So the number of numbers which are ÷ neither by 2 nor by 5
= 1000 – 600
= 400
Three-digit numbers:
| Hundred's | Ten's | Unit |
The unit place can be filed in 4 ways using the digits 1, 3, 7, 9.
Hundred’s place can be filled in 9 ways excluding 0.
Ten’s place can be filled in 10 ways using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
Therefore, the required number of 3 digit numbers neither divisible by 2 nor by 5 is = 9 × 10 × 4 = 360.
There is only one 4-digit number, but it is divisible by 2 and 5.
Therefore, required numbers using fundamental principle of addition = 4 + 36 + 360 = 400
APPEARS IN
संबंधित प्रश्न
A Signal is generated from 2 flags by putting one flag above the other. If 4 flags of different colours are available, how many different signals can be generated?
How many three-digit numbers can be formed from the digits 0, 1, 3, 5, 6 if repetitions of digits are allowed?
How many three-digit numbers can be formed using the digits 2, 3, 4, 5, 6 if digits can be repeated?
How many numbers between 100 and 1000 have the digit 7 exactly once?
How many words can be formed by writing letters in the word CROWN in different order?
Answer the following:
A hall has 12 lamps and every lamp can be switched on independently. Find the number of ways of illuminating the hall.
How many three-digit odd numbers can be formed by using the digits 0, 1, 2, 3, 4, 5? if the repetition of digits is not allowed
Count the numbers between 999 and 10000 subject to the condition that there are no digit is repeated
Count the numbers between 999 and 10000 subject to the condition that there are at least one of the digits is repeated
How many three-digit numbers, which are divisible by 5, can be formed using the digits 0, 1, 2, 3, 4, 5 if repetition of digits are allowed?
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 B1, two different train routes say T1, T2 and one air route A1. Find the number of routes of commuting from place A to place C via place B without using similar mode of transportation
Find the value of `(("n" + 3)!)/(("n" + 1)!)`
Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 10, r = 3
Choose the correct alternative:
The sum of the digits at the 10th place of all numbers formed with the help of 2, 4, 5, 7 taken all at a time is
The number of ways in which a garland can be formed by using 10 identical pink flowers and 9 identical white flowers is ______
In a class, there are 27 boys and 14 girls. The teacher wants to select 1 boy and 1 girl to represent the class for a function. In how many ways can the teacher make this selection?
There will be only 24 selections containing at least one red ball out of a bag containing 4 red and 5 black balls. It is being given that the balls of the same colour are identical.
