Advertisements
Advertisements
Question
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.
Advertisements
Solution
Given that all the 5 digit numbers are greater than 7000.
So, the ways of forming 5-digit numbers = 5 × 4 × 3 × 2 × 1 = 120
Now all the four-digit number greater than 7000 can be formed as follows.
Thousand place can be filled with 3 ways
Hundred place can be filled with 4 ways
Tenths place can be filled with 3 ways
Units place can be filled with 2 ways
So, the total number of 4-digits numbers = 3 × 4 × 3 × 2 = 72
∴ Total number of integers = 120 + 72 = 192
Hence, the required number of integers = 192
APPEARS IN
RELATED QUESTIONS
How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?
How many two-letter words can be formed using letters from the word SPACE, when repetition of letters is not allowed?
A teacher wants to select the class monitor in a class of 30 boys and 20 girls. In how many ways can the monitor be selected if the monitor must be a girl or a boy?
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?
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 4 in the units place?
If numbers are formed using digits 2, 3, 4, 5, 6 without repetition, how many of them will exceed 400?
A school has three gates and four staircases from the first floor to the second floor. How many ways does a student have to go from outside the school to his classroom on the second floor?
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?
In how many ways 5 persons can be seated in a row?
A mobile phone has a passcode of 6 distinct digits. What is the maximum number of attempts one makes to retrieve the passcode?
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 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 n if (n + 1)! = 20(n − 1)!
Find the value of n if `1/(8!) + 1/(9!) = "n"/(10!)`
Choose the correct alternative:
In an examination there are three multiple choice questions and each question has 5 choices. Number of ways in which a student can fail to get all answer correct i
Choose the correct alternative:
The number of 5 digit numbers all digits of which are odd i
Choose the correct alternative:
The number of five digit telephone numbers having at least one of their digits repeated i
The number of ways in which a garland can be formed by using 10 identical pink flowers and 9 identical white flowers 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 ______
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?
In how many ways can this diagram be coloured subject to the following two conditions?
(i) Each of the smaller triangle is to be painted with one of three colours: red, blue or green.
(ii) No two adjacent regions have the same colour.
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?
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.
The sum of the digits in unit place of all the numbers formed with the help of 3, 4, 5 and 6 taken all at a time is ______.
The number of six-digit numbers, all digits of which are odd is ______.
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.
