Advertisements
Advertisements
प्रश्न
Find the number of words formed by permuting all the letters of the following words:
INDIA
उत्तर
This word consists of 5 letters that include two Is.
The total number of words is the number of arrangements of 5 things, of which 2 are similar to one kind.
⇒\[\frac{5!}{2!}\]= 60
APPEARS IN
संबंधित प्रश्न
Convert the following products into factorials:
3 · 6 · 9 · 12 · 15 · 18
Prove that: n! (n + 2) = n! + (n + 1)!
If \[\frac{(2n)!}{3! (2n - 3)!}\] and \[\frac{n!}{2! (n - 2)!}\] are in the ratio 44 : 3, find n.
Prove that:
If P (n, 5) = 20. P(n, 3), find n ?
If P(11, r) = P (12, r − 1) find r.
If P (n, 4) = 12 . P (n, 2), find n.
If P (n − 1, 3) : P (n, 4) = 1 : 9, find n.
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?
Find the number of different 4-letter words, with or without meanings, that can be formed from the letters of the word 'NUMBER'.
How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?
Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, if no digit is repeated? How many of these will be even?
In how many ways can the letters of the word 'STRANGE' be arranged so that
the vowels occupy only the odd places?
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 with the letters of word 'SUNDAY'? How many of the words begin with N? How many begin with N and end in Y?
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 different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:
the vowels always occupy even places?
How many permutations can be formed by the letters of the word, 'VOWELS', when
all consonants come together?
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 4 letters are used at a time?
How many three letter words can be made using the letters of the word 'ORIENTAL'?
How many words can be formed with the letters of the word 'PARALLEL' so that all L's do not come together?
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?
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?
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 ?
Prove that: 4nC2n : 2nCn = [1 · 3 · 5 ... (4n − 1)] : [1 · 3 · 5 ... (2n − 1)]2.
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
If 35Cn +7 = 35C4n − 2 , then write the values of n.
Write the number of diagonals of an n-sided polygon.
Write the maximum number of points of intersection of 8 straight lines in a plane.
Write the number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines.
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.
Write the number of ways in which 12 boys may be divided into three groups of 4 boys each.
Write the total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants.