Advertisements
Advertisements
Question
How many numbers between 100 and 1000 have the digit 7 exactly once?
Advertisements
Solution
Between 100 and 1000 we have all 3-digit numbers and digits used are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
Digit 7 can be placed either in unit's place or in ten's place or in hundred's place.
(i) Digit 7 in unit's place:
Unit's place can be filled in only in 1 way.
Ten's place can be filled in by remaining 9 digits in 9 different ways.
Hundred's place can be filled in by (except '0') remaining 8 digits in 8 different ways.
∴ the total numbers between 100 and 1000 with 7 at unit's place
= 8 × 9 × 1
= 72
(ii) Digit 7 in ten's place:
Unit's place can be filled in by remaining 9 digits (except 7) in 9 different ways.
Ten's place can be filled in by 7 in 1 way only.
Hundred's place can be filled in by remaining 8 digits (except 0 and 7) in 8 different ways .
∴ the total numbers between 100 and 1000 with 7 at ten's place
= 8 × 1 × 9
= 72
(iii) Digit 7 in hundred's place:
Unit's place can be filled in by remaining 9 digits (except 7) in 9 different ways.
Ten's place can be filled in by remaining 9 digits (except 7) in 9 different ways.
Hundred's place can be filled in by digit 7 in only 1 way.
∴ the total numbers between 100 and 1000 with 7 at hundred's place
= 1 × 9 × 9
= 81
Hence, there are 72 + 72 + 81 = 225 numbers between 100 and 1000 such that exactly one of the digits is 7.
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 allowed?
How many three-digit numbers can be formed using the digits 2, 3, 4, 5, 6 if digits can be repeated?
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?
How many numbers between 100 and 1000 have 4 in the units place?
How many four digit numbers will not exceed 7432 if they are formed using the digits 2, 3, 4, 7 without repetition?
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 five-digit numbers formed using the digit 0, 1, 2, 3, 4, 5 are divisible by 5 if digits are not repeated?
Select the correct answer from the given alternatives.
A college offers 5 courses in the morning and 3 in the evening. The number of ways a student can select exactly one course, either in the morning or in the evening
Select the correct answer from the given alternatives.
A college has 7 courses in the morning and 3 in the evening. The possible number of choices with the student if he wants to study one course in the morning and one in the evening is -
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 numbers are there between 100 and 500 with the digits 0, 1, 2, 3, 4, 5? if repetition of digits allowed
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
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 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 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?
Count the total number of ways of answering 6 objective type questions, each question having 4 choices
Find the number of ways of distributing 12 distinct prizes to 10 students?
Find the value of `(12!)/(9! xx 3!)`
Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 6, r = 2
Choose the correct alternative:
The number of ways in which the following prize be given to a class of 30 boys first and second in mathematics, first and second in physics, first in chemistry and first in English is
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 ______
A candidate is required to answer 7 questions out of 12 questions, which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. Find the number of different ways of doing question
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 possible outcomes when a coin is tossed 6 times is ______.
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 ______.
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.
The number of all four digit numbers which begin with 4 and end with either zero or five is ______.
