Advertisements
Advertisements
प्रश्न
If numbers are formed using digits 2, 3, 4, 5, 6 without repetition, how many of them will exceed 400?
उत्तर
Digits are 2, 3, 4, 5, 6.
We have to form the numbers greater than 400.
The repetition of digits is not allowed. The numbers greater than 400 may be of
(i) 3-digit numbers:
For 3-digit numbers greater than 400, hundred's place can be filled either by 4 or 5 or 6.
Hundred's place can be filled by using 4 or 5 or 6 in 3 different ways.
The ten's and unit's place can be filled by remaining digits in 4 and 3 ways respectively.
∴ total number of 3-digit numbers greater than 400
= 3 × 4 × 3
= 36
(ii) 4-digit numbers:
The thousand's place can be filled by anyone of the given 5 digits in 5 different ways.
Since repetition of digits is not allowed, the hundred's place, ten's place, and unit's place can be filled by remaining digits in 4, 3, and 2 ways respectively.
∴ total number of 4-digit numbers
= 5 × 4 × 3 × 2
= 120
(iii) 5-digit numbers:
The ten thousand's place can be filled by anyone of the given 5 digits in 5 different ways.
Since repetition of digits is not allowed, the thousand's place, hundred's place, ten's place, and unit's place can be filled by remaining digits in 4, 3, 2, and 1 way respectively.
∴ total number of 5-digit numbers
= 5 × 4 × 3 × 2 × 1
= 120
Thus, the total numbers greater than 400
= 36 + 120 + 120
= 276
APPEARS IN
संबंधित प्रश्न
Given 5 flags of different colours, how many different signals can be generated if each signal requires the use of 2 flags, one below the other?
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 not allowed?
How many three-digit numbers can be formed using the digits 2, 3, 4, 5, 6 if digits can be repeated?
In a test, 5 questions are of the form 'state, true or false'. No student has got all answers correct. Also, the answer of every student is different. Find the number of students appeared for the test.
How many numbers between 100 and 1000 have 4 in the units place?
How many numbers formed with the digits 0, 1, 2, 5, 7, 8 will fall between 13 and 1000 if digits can be repeated?
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.
A person went to a restaurant for dinner. In the menu card, the person saw 10 Indian and 7 Chinese food items. In how many ways the person can select either an Indian or a Chinese food?
There are 3 types of toy car and 2 types of toy train available in a shop. Find the number of ways a baby can buy a toy car and a toy train?
How many two-digit numbers can be formed using 1, 2, 3, 4, 5 without repetition of digits?
Given four flags of different colours, how many different signals can be generated if each signal requires the use of three flags, one below the other?
How many three-digit numbers are there with 3 in the unit place?
without repetition
How many numbers are there between 100 and 500 with the digits 0, 1, 2, 3, 4, 5? if the repetition of digits is not allowed
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
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
How many numbers are there between 1 and 1000 (both inclusive) which are divisible neither by 2 nor by 5?
How many strings can be formed using the letters of the word LOTUS if the word either starts with L or ends with S?
How many strings can be formed using the letters of the word LOTUS if the word neither starts with L nor ends with S?
Find the value of 6!
Find the value of 3! × 2!
Find the value of `(12!)/(9! xx 3!)`
Find the value of `(("n" + 3)!)/(("n" + 1)!)`
Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 6, r = 2
Find the value of n if `1/(8!) + 1/(9!) = "n"/(10!)`
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
Eight chairs are numbered 1 to 8. Two women and 3 men wish to occupy one chair each. First the women choose the chairs from amongst the chairs 1 to 4 and then men select from the remaining chairs. Find the total number of possible arrangements.
Find the number of positive integers greater than 6000 and less than 7000 which are divisible by 5, provided that no digit is to be repeated.
Find the number of integers greater than 7000 that can be formed with the digits 3, 5, 7, 8 and 9 where no digits are repeated.
The number of different four-digit numbers that can be formed with the digits 2, 3, 4, 7 and using each digit only once is ______.
Three letters can be posted in five letterboxes in 35 ways.
In a steamer there are stalls for 12 animals, and there are horses, cows and calves (not less than 12 each) ready to be shipped. They can be loaded in 312 ways.
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.
