Advertisements
Advertisements
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.
Advertisements
Solution
Any number divisible by 5, its unit place must have 0 or 5 We have to find 4-digit number greater than 6000 and less than 7000.
So, the unit place can be filled with 2 ways (0 or 5) since, repetition is not allowed
∴ Tens place can be filled with 7 ways and hundreds place can be filled with 8 ways.
But the required number is greater than 6000 and less than 7000.
So, thousand place can be filled with 1 digits i.e. 6
Th H T O
1 8 7 2
So, the total number of integers = 1 × 8 × 7 × 2 = 112
Hence, the required number of integers = 112
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 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 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?
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 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?
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?
Three persons enter into a conference hall in which there are 10 seats. In how many ways they can take their seats?
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?
Four children are running a race:
In how many ways can the first two places be filled?
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 allowed
How many three-digit numbers are there with 3 in the unit place?
with repetition
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 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
Count the numbers between 999 and 10000 subject to the condition that there are at least one of the digits is repeated
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 3! – 2!
Find the value of `(12!)/(9! xx 3!)`
Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 10, r = 3
Choose the correct alternative:
The sum of the digits at the 10th place of all numbers formed with the help of 2, 4, 5, 7 taken all at a time 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 ______
How many numbers are there between 99 and 1000 having 7 in the units place?
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.
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.
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 integers greater than 7000 that can be formed with the digits 3, 5, 7, 8 and 9 where no digits are repeated.
If the number of five-digit numbers with distinct digits and 2 at the 10th place is 336 k, then k is equal to ______.
