Advertisements
Advertisements
Question
The sum of the digits in unit place of all the numbers formed with the help of 3, 4, 5 and 6 taken all at a time is ______.
Options
432
108
36
18
Advertisements
Solution
The sum of the digits in unit place of all the numbers formed with the help of 3, 4, 5 and 6 taken all at a time is 108.
Explanation:
If we fix 3 at unit place, then the total possible numbers = 3!
If we fix 4, 5 and 6 at unit place, this is each case, total possible numbers are 3!
Required sum of unit digits of all such numbers is
= 3 × 3! + 4 × 3! + 5 × 3! + 6 × 3!
= (3 + 4 + 5 + 6) × 3!
= 18 × 3!
= 18 × 3 × 2 × 1
= 108
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?
Given 5 flags of different colours, how many different signals can be generated if each signal requires the use of 2 flags, one below the other?
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 not allowed?
How many two letter words can be formed using letters from the word SPACE, when repetition of letters is 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 4 in the units place?
How many four digit numbers will not exceed 7432 if they are formed using the digits 2, 3, 4, 7 without repetition?
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?
A school has three gates and four staircases from the first floor to the second floor. How many ways does a student have to go from outside the school to his classroom on the second floor?
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?
How many two-digit numbers can be formed using 1, 2, 3, 4, 5 without repetition of digits?
Three persons enter into a conference hall in which there are 10 seats. In how many ways they can take their seats?
How many three-digit numbers are there with 3 in the unit place?
without 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
Count the numbers between 999 and 10000 subject to the condition that there are no restriction
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?
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
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 3! – 2!
Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 6, r = 2
Find the value of n if `1/(8!) + 1/(9!) = "n"/(10!)`
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 atleast one of their digits 7?
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?
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
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.
