Advertisements
Advertisements
प्रश्न
How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?
Advertisements
उत्तर
There will be as many ways as there are ways of filling 3 vacant places
in succession with the given six digits. In this case, the units place can be filled by 2 or 4 or 6 only, i.e., the units place can be filled in 3 ways. The tens place can be filled by any of the 6 digits in 6 different ways and the hundreds place can be filled by any of the 6 digits in 6 different ways, as the digits can be repeated.
Therefore, by the multiplication principle, the required number of three digit even numbers is 3 × 6 × 6 = 108.
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 not allowed?
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 numbers between 100 and 1000 have 4 in the units place?
How many numbers between 100 and 1000 have the digit 7 exactly once?
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 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?
How many three-digit numbers can be formed using the digits 2, 3, 4, 5, 6 if digits can be repeated?
In a test, 5 questions are of the form 'state, true or false'. No student has got all answers correct. Also, the answer of every student is different. Find the number of students appeared for the test.
How many numbers formed with the digits 0, 1, 2, 5, 7, 8 will fall between 13 and 1000 if digits can be repeated?
Answer the following:
A hall has 12 lamps and every lamp can be switched on independently. Find the number of ways of illuminating the hall.
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?
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?
Four children are running a race:
In how many different ways could they finish the race?
How many three-digit numbers are there with 3 in the unit place?
without repetition
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 digit is repeated
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 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!
Find the value of 3! – 2!
Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 10, r = 3
Evaluate `("n"!)/("r"!("n" - "r")!)` when for any n with r = 2
Find the value of n if (n + 1)! = 20(n − 1)!
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
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?
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.
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 integers greater than 7000 that can be formed with the digits 3, 5, 7, 8 and 9 where no digits are repeated.
The number of possible outcomes when a coin is tossed 6 times is ______.
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 ______.
The number of six-digit numbers, all digits of which are odd is ______.
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.
