Advertisements
Advertisements
प्रश्न
How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?
Advertisements
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
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 r if `""^5P_r = 2^6 P_(r-1)`
How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if
(i) 4 letters are used at a time,
(ii) all letters are used at a time,
(iii) all letters are used but first letter is a vowel?
In how many ways can the letters of the word PERMUTATIONS be arranged if the vowels are all together.
Find x in each of the following:
In how many ways can three jobs I, II and III be assigned to three persons A, B and C if one person is assigned only one job and all are capable of doing each job?
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 ?
In how many ways can 5 different balls be distributed among three boxes?
In how many ways 4 women draw water from 4 taps, if no tap remains unused?
Write the number of words that can be formed out of the letters of the word 'COMMITTEE' ?
Write the number of numbers that can be formed using all for digits 1, 2, 3, 4 ?
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
How many six-digit telephone numbers can be formed if the first two digits are 45 and no digit can appear more than once?
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?
Find the rank of the word ‘CHAT’ in the dictionary.
Evaluate the following.
`((3!)! xx 2!)/(5!)`
The possible outcomes when a coin is tossed five times:
If n is a positive integer, then the number of terms in the expansion of (x + a)n is:
The total number of 9 digit number which has all different digit is:
If `""^10"P"_("r" - 1)` = 2 × 6Pr, find r
Three men have 4 coats, 5 waist coats and 6 caps. In how many ways can they wear them?
Determine the number of permutations of the letters of the word SIMPLE if all are taken at a time?
A test consists of 10 multiple choice questions. In how many ways can the test be answered if each question has four choices?
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?
8 women and 6 men are standing in a line. In how many arrangements will no two men be standing next to one another?
In how many ways 4 mathematics books, 3 physics books, 2 chemistry books and 1 biology book can be arranged on a shelf so that all books of the same subjects are together
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 of heads and tails are possible?
How many strings are there using the letters of the word INTERMEDIATE, if the vowels and consonants are alternative
Choose the correct alternative:
If `""^(("n" + 5))"P"_(("n" + 1)) = ((11("n" - 1))/2)^(("n" + 3))"P"_"n"`, then the value of n are
In how many ways can 5 children be arranged in a line such that two particular children of them are always together
If all permutations of the letters of the word AGAIN are arranged in the order as in a dictionary. What is the 49th word?
If 1P1 + 2. 2p2 + 3. 3p3 + ....... 15. 15P15 = qPr – s, 0 ≤ s ≤ 1, then q+sCr–s is equal to ______.
If m+nP2 = 90 and m–nP2 = 30, then (m, n) is given by ______.
