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 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?
How many three-digit numbers can be formed from the digits 0, 1, 3, 5, 6 if repetitions of digits are allowed?
How many three-digit numbers can be formed using the digits 2, 3, 4, 5, 6 if digits can be repeated?
If numbers are formed using digits 2, 3, 4, 5, 6 without repetition, how many of them will exceed 400?
How many numbers formed with the digits 0, 1, 2, 5, 7, 8 will fall between 13 and 1000 if digits can be repeated?
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?
Four children are running a race:
In how many different ways could they finish the race?
Count the number of three-digit numbers which can be formed from the digits 2, 4, 6, 8 if repetitions of digits is not allowed
How many numbers are there between 100 and 500 with the digits 0, 1, 2, 3, 4, 5? if repetition of digits allowed
In how many ways 10 pigeons can be placed in 3 different pigeon holes?
Find the number of ways of distributing 12 distinct prizes to 10 students?
Find the value of 4! + 5!
Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 6, r = 2
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?
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
Three letters can be posted in five letterboxes in 35 ways.
If the number of five-digit numbers with distinct digits and 2 at the 10th place is 336 k, then k is equal to ______.
