Advertisements
Advertisements
Question
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?
Advertisements
Solution
There will be as many ways as there are ways of filling 3 vacant 
places in succession with the five given digits.
In succession by the given five digits. In this case, repetition of digits is allowed. Therefore, the unit place can be filled in by any of the given five digits. Similarly, tens and hundreds digits can be filled in by any of the given five digits.
Thus, by the multiplication principle, the number of ways in which three-digit numbers can be formed from the given digits is 5 × 5 × 5 = 125.
APPEARS IN
RELATED QUESTIONS
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 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?
A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?
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 not allowed?
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 using the digits 2, 3, 4, 5, 6 if digits can be repeated?
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?
If numbers are formed using digits 2, 3, 4, 5, 6 without repetition, how many of them will exceed 400?
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?
Count the number of three-digit numbers which can be formed from the digits 2, 4, 6, 8 if repetitions of digits is allowed
Count the number of three-digit numbers which can be formed from the digits 2, 4, 6, 8 if repetitions of digits is not allowed
How many three-digit numbers are there with 3 in the unit place?
with repetition
Count the numbers between 999 and 10000 subject to the condition that there are no digit is repeated
Count the numbers between 999 and 10000 subject to the condition that there are at least one of the digits is repeated
How many strings can be formed using the letters of the word LOTUS if the word either starts with L or ends with S?
Find the value of 3! × 2!
Find the value of `(("n" + 3)!)/(("n" + 1)!)`
Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 6, 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
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:
The number of 10 digit number that can be written by using the digits 2 and 3 is
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?
In an examination there are three multiple choice questions and each question has 4 choices. Number of ways in which a student can fail to get all answer correct is ______.
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.
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.
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.
If the number of five-digit numbers with distinct digits and 2 at the 10th place is 336 k, then k is equal to ______.
