Advertisements
Advertisements
प्रश्न
If numbers are formed using digits 2, 3, 4, 5, 6 without repetition, how many of them will exceed 400?
Advertisements
उत्तर
Digits are 2, 3, 4, 5, 6.
We have to form the numbers greater than 400.
The repetition of digits is not allowed. The numbers greater than 400 may be of
(i) 3-digit numbers:
For 3-digit numbers greater than 400, hundred's place can be filled either by 4 or 5 or 6.
Hundred's place can be filled by using 4 or 5 or 6 in 3 different ways.
The ten's and unit's place can be filled by remaining digits in 4 and 3 ways respectively.
∴ total number of 3-digit numbers greater than 400
= 3 × 4 × 3
= 36
(ii) 4-digit numbers:
The thousand's place can be filled by anyone of the given 5 digits in 5 different ways.
Since repetition of digits is not allowed, the hundred's place, ten's place, and unit's place can be filled by remaining digits in 4, 3, and 2 ways respectively.
∴ total number of 4-digit numbers
= 5 × 4 × 3 × 2
= 120
(iii) 5-digit numbers:
The ten thousand's place can be filled by anyone of the given 5 digits in 5 different ways.
Since repetition of digits is not allowed, the thousand's place, hundred's place, ten's place, and unit's place can be filled by remaining digits in 4, 3, 2, and 1 way respectively.
∴ total number of 5-digit numbers
= 5 × 4 × 3 × 2 × 1
= 120
Thus, the total numbers greater than 400
= 36 + 120 + 120
= 276
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 numbers between 100 and 1000 have 4 in the units place?
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?
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 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?
How many numbers between 100 and 1000 have the digit 7 exactly once?
How many four digit numbers will not exceed 7432 if they are formed using the digits 2, 3, 4, 7 without repetition?
How many numbers formed with the digits 0, 1, 2, 5, 7, 8 will fall between 13 and 1000 if digits can be repeated?
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
A person went to a restaurant for dinner. In the menu card, the person saw 10 Indian and 7 Chinese food items. In how many ways the person can select either an Indian or a Chinese food?
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?
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?
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 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
Count the numbers between 999 and 10000 subject to the condition that there are no restriction
Find the value of 6!
Find the value of 3! × 2!
Find the value of `(12!)/(9! xx 3!)`
Find the value of `(("n" + 3)!)/(("n" + 1)!)`
Evaluate `("n"!)/("r"!("n" - "r")!)` when for any n with r = 2
Find the value of n if `1/(8!) + 1/(9!) = "n"/(10!)`
Choose the correct alternative:
In an examination there are three multiple choice questions and each question has 5 choices. Number of ways in which a student can fail to get all answer correct i
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
Choose the correct alternative:
The number of 10 digit number that can be written by using the digits 2 and 3 is
How many numbers are there between 99 and 1000 having atleast one of their digits 7?
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
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.
The number of six-digit numbers, all digits of which are odd is ______.
Three letters can be posted in five letterboxes in 35 ways.
There will be only 24 selections containing at least one red ball out of a bag containing 4 red and 5 black balls. It is being given that the balls of the same colour are identical.
