Advertisements
Advertisements
Question
Count the numbers between 999 and 10000 subject to the condition that there are no digit is repeated
Advertisements
Solution
Since 0 is given as a digit
We have to start filling 1000’s place.
Now 1000’s place can be filled in 9 ways (excluding 0)
Then the 100’s place can be filled in 9 ways (excluding one digit and including 0)
10’s place can be filled in (9 – 1)8 ways and unit place can be filled in (8 – 1)7 ways
So the number of 4 digit numbers are 9 × 9 × 8 × 7 = 4536 ways
APPEARS IN
RELATED QUESTIONS
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?
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 two letter words can be formed using letters from the word SPACE, when repetition of letters is allowed?
How many numbers between 100 and 1000 have the digit 7 exactly once?
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 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?
How many numbers between 100 and 1000 have the digit 7 exactly once?
Three persons enter into a conference hall in which there are 10 seats. In how many ways they can take their seats?
In how many ways 5 persons can be seated in a row?
How many three-digit numbers are there with 3 in the unit place?
with repetition
Find the value of n if (n + 1)! = 20(n − 1)!
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
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.
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?
Out of 18 points in a plane, no three are in the same line except five points which are collinear. Find the number of lines that can be formed joining the point
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.
