Advertisements
Advertisements
Question
How many three-digit numbers are there, with no digit repeated?
Advertisements
Solution
Total number of 3-digit numbers = Number of arrangements of 10 numbers, taken 3 at a time = 10P3 =\[\frac{10!}{7!} = 10 \times 9 \times 8 = 720\]
Total number of 3-digit numbers, having 0 at its hundred's place = 9P2 =\[\frac{9!}{7!} = 9 \times 8 = 72\]
Total number of 3-digit numbers with distinct digits = 10P3\[-\] 9P2 = 720\[-\] 72 = 648
APPEARS IN
RELATED QUESTIONS
If (n + 1)! = 90 [(n − 1)!], find n.
Prove that:
Prove that:
\[\frac{n!}{(n - r)! r!} + \frac{n!}{(n - r + 1)! (r - 1)!} = \frac{(n + 1)!}{r! (n - r + 1)!}\]
If P(11, r) = P (12, r − 1) find r.
If P (n − 1, 3) : P (n, 4) = 1 : 9, find n.
If P (2n − 1, n) : P (2n + 1, n − 1) = 22 : 7 find n.
Prove that:1 . P (1, 1) + 2 . P (2, 2) + 3 . P (3, 3) + ... + n . P (n, n) = P (n + 1, n + 1) − 1.
If P (15, r − 1) : P (16, r − 2) = 3 : 4, find r.
From among the 36 teachers in a school, one principal and one vice-principal are to be appointed. In how many ways can this be done?
Four books, one each in Chemistry, Physics, Biology and Mathematics, are to be arranged in a shelf. In how many ways can this be done?
How many words, with or without meaning, can be formed by using all the letters of the word 'DELHI', using each letter exactly once?
How many words, with or without meaning, can be formed by using the letters of the word 'TRIANGLE'?
In how many ways can 6 boys and 5 girls be arranged for a group photograph if the girls are to sit on chairs in a row and the boys are to stand in a row behind them?
All the letters of the word 'EAMCOT' are arranged in different possible ways. Find the number of arrangements in which no two vowels are adjacent to each other.
How many words can be formed out of the letters of the word, 'ORIENTAL', so that the vowels always occupy the odd places?
How many different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:
the letters P and I respectively occupy first and last place?
How many permutations can be formed by the letters of the word, 'VOWELS', when
each word begins with E?
How many words can be formed out of the letters of the word 'ARTICLE', so that vowels occupy even places?
Find the number of words formed by permuting all the letters of the following words:
CONSTANTINOPLE
How many numbers can be formed with the digits 1, 2, 3, 4, 3, 2, 1 so that the odd digits always occupy the odd places?
How many number of four digits can be formed with the digits 1, 3, 3, 0?
How many different numbers, greater than 50000 can be formed with the digits 0, 1, 1, 5, 9.
How many permutations of the letters of the word 'MADHUBANI' do not begin with M but end with I?
There are three copies each of 4 different books. In how many ways can they be arranged in a shelf?
How many numbers greater than 1000000 can be formed by using the digits 1, 2, 0, 2, 4, 2, 4?
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S's are together?
Find the total number of permutations of the letters of the word 'INSTITUTE'.
The letters of the word 'SURITI' are written in all possible orders and these words are written out as in a dictionary. Find the rank of the word 'SURITI'.
If the letters of the word 'LATE' be permuted and the words so formed be arranged as in a dictionary, find the rank of the word LATE.
If the permutations of a, b, c, d, e taken all together be written down in alphabetical order as in dictionary and numbered, find the rank of the permutation debac ?
In how many ways can the letters of the word
"INTERMEDIATE" be arranged so that:the vowels always occupy even places?
The letters of the word 'ZENITH' are written in all possible orders. How many words are possible if all these words are written out as in a dictionary? What is the rank of the word 'ZENITH'?
Prove that the product of 2n consecutive negative integers is divisible by (2n)!
For all positive integers n, show that 2nCn + 2nCn − 1 = `1/2` 2n + 2Cn+1
How many words, with or without meaning can be formed from the letters of the word 'MONDAY', assuming that no letter is repeated, if (i) 4 letters are used at a time
Write the expression nCr +1 + nCr − 1 + 2 × nCr in the simplest form.
