Advertisements
Advertisements
प्रश्न
How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?
उत्तर
3-digit numbers have to be formed using the digits 1 to 9.
Here, the order of the digits matters.
Therefore, there will be as many 3-digit numbers as there are permutations of 9 different digits taken 3 at a time.
Therefore, required number of 3-digit numbers
= 9P3 = `(9!)/((9 - 3)!) = (9!)/(6!)`
= `(9 xx 8 xx 7 xx 6!)/(6!)`
= 9 x 8 x 7 = 504
APPEARS IN
संबंधित प्रश्न
Find r if `""^5P_r = 2^6 P_(r-1)`
Find r if `""^5P_r = 2^6 P_(r-1)`
Find r if `""^5P_r = ""^6P_(r-1)`
Find x in each of the following:
Find x in each of the following:
How many natural numbers not exceeding 4321 can be formed with the digits 1, 2, 3 and 4, if the digits can repeat?
A coin is tossed three times and the outcomes are recorded. How many possible outcomes are there? How many possible outcomes if the coin is tossed four times? Five times? n times?
How many numbers of four digits can be formed with the digits 1, 2, 3, 4, 5 if the digits can be repeated in the same number?
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?
In how many ways can 4 letters be posted in 5 letter boxes?
Write the number of ways in which 6 men and 5 women can dine at a round table if no two women sit together ?
The number of permutations of n different things taking r at a time when 3 particular things are to be included is
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 in which 6 men can be arranged in a row so that three particular men are consecutive, is
Find x if `1/(6!) + 1/(7!) = x/(8!)`
Find the rank of the word ‘CHAT’ in the dictionary.
The total number of 9 digit number which has all different digit is:
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 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?
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. 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?
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 of these 6-digit numbers are divisible by 4?
Find the sum of all 4-digit numbers that can be formed using digits 1, 2, 3, 4, and 5 repetitions not allowed?
Find the sum of all 4-digit numbers that can be formed using digits 0, 2, 5, 7, 8 without repetition?
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
In how many ways can 5 children be arranged in a line such that two particular children of them are never together.
The number of signals that can be sent by 6 flags of different colours taking one or more at a time is ______.
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 words which can be formed out of the letters of the word ARTICLE, so that vowels occupy the even place is ______.
Let b1, b2, b3, b4 be a 4-element permutation with bi ∈ {1, 2, 3, .......,100} for 1 ≤ i ≤ 4 and bi ≠ bj for i ≠ j, such that either b1, b2, b3 are consecutive integers or b2, b3, b4 are consecutive integers. Then the number of such permutations b1, b2, b3, b4 is equal to ______.
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.
