Advertisements
Advertisements
Question
How many natural numbers not exceeding 4321 can be formed with the digits 1, 2, 3 and 4, if the digits can repeat?
Advertisements
Solution
Case I: Four-digit number
Total number of ways in which the 4 digit number can be formed =`4xx4xx4xx4=256`
Now, the number of ways in which the 4-digit numbers greater than 4321 can be formed is as follows:
Suppose, the thousand's digit is 4 and hundred's digit is either 3 or 4.
∴ Number of ways =`2xx4xx4=32`
But 4311, 4312, 4313, 4314, 4321 (i.e. 5 numbers) are less than or equal to 4321.
∴ Remaining number of ways =`256-(32-5)=229`
Case II: Three-digit number
The hundred's digit can be filled in 4 ways.
Similarly, the ten's digit and the unit's digit can also be filled in 4 ways each. This is because the repetition of digits is allowed.
∴ Total number of three-digit number =`4xx4xx4=64`
Case III: Two-digit number
The ten's digit and the unit's digit can be filled in 4 ways each. This is because the repetition of digits is allowed.
∴ Total number of two digit numbers `4xx4=16`
Case IV: One-digit number
Single digit number can only be four.
∴ Required numbers = 229 + 64 + 16 +4 = 313
APPEARS IN
RELATED QUESTIONS
Evaluate 8!
Evaluate 4! – 3!
Compute `(8!)/(6! xx 2!)`
Find n if n – 1P3 : nP4 = 1 : 9
Find x in each of the following:
Find the number of ways in which 8 distinct toys can be distributed among 5 childrens.
Three dice are rolled. Find the number of possible outcomes in which at least one die shows 5 ?
Evaluate each of the following:
6P6
Write the number of arrangements of the letters of the word BANANA in which two N's come together.
Write the number of ways in which 5 boys and 3 girls can be seated in a row so that each girl is between 2 boys ?
Write the remainder obtained when 1! + 2! + 3! + ... + 200! is divided by 14 ?
The number of words from the letters of the word 'BHARAT' in which B and H will never come together, is
If the letters of the word KRISNA are arranged in all possible ways and these words are written out as in a dictionary, then the rank of the word KRISNA is
A 5-digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways in which this can be done is
In a room there are 12 bulbs of the same wattage, each having a separate switch. The number of ways to light the room with different amounts of illumination is
English alphabet has 11 symmetric letters that appear same when looked at in a mirror. These letters are A, H, I, M, O, T, U, V, W, X and Y. How many symmetric three letters passwords can be formed using these letters?
Find x if `1/(6!) + 1/(7!) = x/(8!)`
How many numbers lesser than 1000 can be formed using the digits 5, 6, 7, 8, and 9 if no digit is repeated?
The greatest positive integer which divide n(n + 1) (n + 2) (n + 3) for all n ∈ N is:
For all n > 0, nC1 + nC2 + nC3 + …… + nCn is equal to:
The number of ways to arrange the letters of the word “CHEESE”:
The number of words with or without meaning that can be formed using letters of the word “EQUATION”, with no repetition of letters is:
Suppose 8 people enter an event in a swimming meet. In how many ways could the gold, silver and bronze prizes be awarded?
A test consists of 10 multiple choice questions. In how many ways can the test be answered if the first four questions have three choices and the remaining have five choices?
A student appears in an objective test which contain 5 multiple choice questions. Each question has four choices out of which one correct answer.
What is the maximum number of different answers can the students give?
A student appears in an objective test which contain 5 multiple choice questions. Each question has four choices out of which one correct answer.
How will the answer change if each question may have more than one correct answers?
How many strings can be formed from the letters of the word ARTICLE, so that vowels occupy the even places?
8 women and 6 men are standing in a line. How many arrangements are possible if any individual can stand in any position?
In how many ways can the letters of the word SUCCESS be arranged so that all Ss are together?
How many strings are there using the letters of the word INTERMEDIATE, if all the vowels are together
How many strings are there using the letters of the word INTERMEDIATE, if vowels are never together
If the letters of the word GARDEN are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, then find the ranks of the words
GARDEN
Find the sum of all 4-digit numbers that can be formed using digits 1, 2, 3, 4, and 5 repetitions not allowed?
Ten different letters of alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have atleast one letter repeated is ______.
Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.
There are 10 persons named P1, P2, P3, ... P10. Out of 10 persons, 5 persons are to be arranged in a line such that in each arrangement P1 must occur whereas P4 and P5 do not occur. Find the number of such possible arrangements.
The number of different words that can be formed from the letters of the word INTERMEDIATE such that two vowels never come together is ______.
Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Determine the number of words which have at least one letter repeated.
