Advertisements
Advertisements
Question
If numbers are formed using digits 2, 3, 4, 5, 6 without repetition, how many of them will exceed 400?
Advertisements
Solution
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
RELATED QUESTIONS
How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?
How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?
A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?
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 two-letter words can be formed using letters from the word SPACE, when repetition of letters is not allowed?
How many numbers between 100 and 1000 have 4 in the units place?
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 two letter words can be formed using letters from the word SPACE, when repetition of letters is allowed?
How many three-digit numbers can be formed from the digits 0, 1, 3, 5, 6 if repetitions of digits are not allowed?
A letter lock contains 3 rings, each ring containing 5 different letters. Determine the maximum number of false trials that can be made before the lock is opened?
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 the digit 7 exactly once?
How many numbers formed with the digits 0, 1, 2, 5, 7, 8 will fall between 13 and 1000 if digits can be repeated?
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 numbers are there with 3 in the unit place?
with repetition
Count the numbers between 999 and 10000 subject to the condition that there are no restriction
Count the numbers between 999 and 10000 subject to the condition that there are no digit 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 not allowed?
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?
Count the total number of ways of answering 6 objective type questions, each question having 4 choices
In how many ways 10 pigeons can be placed in 3 different pigeon holes?
Find the value of 4! + 5!
Find the value of `(12!)/(9! xx 3!)`
Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 6, r = 2
Evaluate `("n"!)/("r"!("n" - "r")!)` when for any n with r = 2
Choose the correct alternative:
The number of 5 digit numbers all digits of which are odd i
Choose the correct alternative:
There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two points is
All the letters of the word PADMAPRIYA are placed at random in a row. The probability that the word PRIY A occurs without getting split is ______
How many numbers are there between 99 and 1000 having 7 in the units place?
There are four bus routes between A and B; and three bus routes between B and C. A man can travel round-trip in number of ways by bus from A to C via B. If he does not want to use a bus route more than once, in how many ways can he make round trip?
If the letters of the word RACHIT are arranged in all possible ways as listed in dictionary. Then what is the rank of the word RACHIT?
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 ______.
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.
