Advertisements
Advertisements
प्रश्न
How many natural numbers less than 1000 can be formed from the digits 0, 1, 2, 3, 4, 5 when a digit may be repeated any number of times?
Advertisements
उत्तर
Since the number is less than 1000, it means that it is a three-digit number, a two-digit number or a single-digit number.
Three-digit numbers:
The hundred's place can be filled by 5 digits neglecting zero as it can't be zero.
The ten's place and the unit's place can be filled by 6 digits.
So, total number of three digit numbers = `5xx6xx6=180`
Two-digit numbers:
The ten's place can be filled by 5 digits, except zero.
The unit's digit can be filled by 6 digits.
Total two digit numbers =`5xx6=30`
Single digit numbers are 1, 2, 3, 4, 5 as 0 is not a natural number. Thus, on neglecting it, we get 5 numbers.
Total required numbers =`180+30+5=215`
APPEARS IN
संबंधित प्रश्न
Compute `(8!)/(6! xx 2!)`
How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?
From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person cannot hold more than one position?
Find n if n – 1P3 : nP4 = 1 : 9
In how many ways can the letters of the word PERMUTATIONS be arranged if the vowels are all together.
How many numbers of six digits can be formed from the digits 0, 1, 3, 5, 7 and 9 when no digit is repeated? How many of them are divisible by 10 ?
How many 5-digit telephone numbers can be constructed using the digits 0 to 9. If each number starts with 67 and no digit appears more than once?
In how many ways can 7 letters be posted in 4 letter boxes?
Write the number of 5 digit numbers that can be formed using digits 0, 1 and 2 ?
In how many ways 4 women draw water from 4 taps, if no tap remains unused?
Write the number of all possible words that can be formed using the letters of the word 'MATHEMATICS'.
The number of words from the letters of the word 'BHARAT' in which B and H will never come together, is
The number of ways to arrange the letters of the word CHEESE are
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
The number of ways in which 6 men can be arranged in a row so that three particular men are consecutive, is
If k + 5Pk + 1 =\[\frac{11 (k - 1)}{2}\]. k + 3Pk , then the values of k are
The number of arrangements of the letters of the word BHARAT taking 3 at a time 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?
How many 6-digit telephone numbers can be constructed with the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 if each numbers starts with 35 and no digit appear more than once?
- In how many ways can 8 identical beads be strung on a necklace?
- In how many ways can 8 boys form a ring?
Find the rank of the word ‘CHAT’ in the dictionary.
Evaluate the following.
`(3! + 1!)/(2^2!)`
For all n > 0, nC1 + nC2 + nC3 + …… + nCn is equal to:
If `""^(("n" – 1))"P"_3 : ""^"n""P"_4` = 1 : 10 find n
8 women and 6 men are standing in a line. In how many arrangements will no two men be standing next to one another?
How many ways can the product a2 b3 c4 be expressed without exponents?
In how many ways can the letters of the word SUCCESS be arranged so that all Ss are together?
A coin is tossed 8 times, how many different sequences containing six heads and two tails are possible?
Each of the digits 1, 1, 2, 3, 3 and 4 is written on a separate card. The six cards are then laid out in a row to form a 6-digit number. How many distinct 6-digit numbers are there?
Find the number of strings that can be made using all letters of the word THING. If these words are written as in a dictionary, what will be the 85th string?
Choose the correct alternative:
If `""^(("n" + 5))"P"_(("n" + 1)) = ((11("n" - 1))/2)^(("n" + 3))"P"_"n"`, then the value of n are
Choose the correct alternative:
The product of r consecutive positive integers is divisible b
Choose the correct alternative:
If Pr stands for rPr then the sum of the series 1 + P1 + 2P2 + 3P3 + · · · + nPn is
Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.
In a certain city, all telephone numbers have six digits, the first two digits always being 41 or 42 or 46 or 62 or 64. How many telephone numbers have all six digits distinct?
The number of 5-digit telephone numbers having atleast one of their digits repeated is ______.
The number of words which can be formed out of the letters of the word ARTICLE, so that vowels occupy the even place is ______.
The number of three-digit even numbers, formed by the digits 0, 1, 3, 4, 6, 7 if the repetition of digits is not allowed, is ______.
