Advertisements
Advertisements
प्रश्न
How many number of four digits can be formed with the digits 1, 3, 3, 0?
Advertisements
उत्तर
The given digits are 1, 3, 3, 0.
Total numbers that can be formed with these digits =\[\frac{4!}{2!}\]Now, these numbers also include the numbers in which the thousand's place is 0.
But, to form a four digit number, this is not possible.
∴ Numbers in which the thousand's place is fixed as zero = Ways of arranging the remaining digits (1,3 and 3) in three places =\[\frac{3!}{2!}\]
∴ Four digit numbers = Total numbers\[-\] Numbers in which the thousand's place is 0=\[\frac{4!}{2!}\]-\[\frac{3!}{2!}\]= 9
APPEARS IN
संबंधित प्रश्न
Convert the following products into factorials:
(n + 1) (n + 2) (n + 3) ... (2n)
Convert the following products into factorials:
1 · 3 · 5 · 7 · 9 ... (2n − 1)
Prove that: n! (n + 2) = n! + (n + 1)!
If (n + 2)! = 60 [(n − 1)!], find n.
Prove that:
If P (5, r) = P (6, r − 1), find r ?
If P (9, r) = 3024, 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?
How many words, with or without meaning, can be formed by using the letters of the word 'TRIANGLE'?
How many three-digit numbers are there, with no digit repeated?
In how many ways can the letters of the word 'STRANGE' be arranged so that
the vowels come together?
In how many ways can the letters of the word 'STRANGE' be arranged so that
the vowels occupy only the odd places?
How many different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:
the letter G always occupies the first place?
How many permutations can be formed by the letters of the word, 'VOWELS', when
there is no restriction on letters?
In how many ways can a lawn tennis mixed double be made up from seven married couples if no husband and wife play in the same set?
How many words (with or without dictionary meaning) can be made from the letters in the word MONDAY, assuming that no letter is repeated, if all letters are used at a time.
How many words (with or without dictionary meaning) can be made from the letters in the word MONDAY, assuming that no letter is repeated, if all letters are used but first is vowel.
Find the number of words formed by permuting all the letters of the following words:
PAKISTAN
Find the number of words formed by permuting all the letters of the following words:
RUSSIA
Find the number of words formed by permuting all the letters of the following words:
SERIES
How many words can be formed with the letters of the word 'PARALLEL' so that all L's do not come together?
How many words can be formed by arranging the letters of the word 'MUMBAI' so that all M's come together?
How many words can be formed from the letters of the word 'SERIES' which start with S and end with S?
There are three copies each of 4 different books. In how many ways can they be arranged in a shelf?
Find the total number of permutations of the letters of the word 'INSTITUTE'.
In how many ways can the letters of the word
"INTERMEDIATE" be arranged so that:the vowels always occupy even places?
Prove that the product of 2n consecutive negative integers is divisible by (2n)!
Evaluate
Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:
n · n − 1Cr − 1 = (n − r + 1) nCr − 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
How many words, with or without meaning can be formed from the letters of the word 'MONDAY', assuming that no letter is repeated, if all letters are used at a time
How many words, with or without meaning can be formed from the letters of the word 'MONDAY', assuming that no letter is repeated, if all letters are used but first letter is a vowel?
Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.
Write the expression nCr +1 + nCr − 1 + 2 × nCr in the simplest form.
Write the number of ways in which 5 red and 4 white balls can be drawn from a bag containing 10 red and 8 white balls.
