Advertisements
Advertisements
प्रश्न
How many numbers between 100 and 1000 have the digit 7 exactly once?
Advertisements
उत्तर
A number between 100 and 1000 are 3-digit numbers.
A 3-digit number is to be formed from the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, where exactly one of the digits is 7.
Let us consider the three cases separately.
Case (I): the digit 7 is in the unit’s place.
The ten’s place is filled by one digit from 0 to excluding 7 in 9 ways.
Here, there are 8 × 9 × 1 = 72 three digit numbers with the required condition.
Case (II): The digit 7 is in the ten’s place.
Unit’s place can be filled by digit from 0 to 9 excluding 7 in 9 ways.
Zero is not allowed at a hundred’s place.
Hundred's place can be filled by digit from 1 to 9 excluding 7 in 8 ways.
The hundred’s place can be filled in by any digit from 1 to 9 excluding 7 in 8 ways.
Here, there will be 8 × 1 × 9 = 72
3-digit numbers with the required condition
Case (III): The digit 7 is in the hundred’s place.
Then, there are 1 × 9 × 9 = 81
3-digit numbers with the required condition.
Hence, the numbers between 100 and 1000 having the digit 7 exactly once are 72 + 72 + 81 = 225.
APPEARS IN
संबंधित प्रश्न
How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is allowed?
How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits 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?
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
How many words can be formed by writing letters in the word CROWN in different order?
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?
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?
Four children are running a race:
In how many ways can the first two places be filled?
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
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 not allowed?
Find the value of 4! + 5!
Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 6, r = 2
Evaluate `("n"!)/("r"!("n" - "r")!)` when for any n with r = 2
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.
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.
The number of all four digit numbers which begin with 4 and end with either zero or five is ______.
