Advertisements
Advertisements
प्रश्न
Find the number of words formed by permuting all the letters of the following words:
INDIA
Advertisements
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
Prove that: n! (n + 2) = n! + (n + 1)!
If (n + 3)! = 56 [(n + 1)!], find n.
Prove that:
\[\frac{n!}{(n - r)! r!} + \frac{n!}{(n - r + 1)! (r - 1)!} = \frac{(n + 1)!}{r! (n - r + 1)!}\]
If 5 P(4, n) = 6. P (5, n − 1), find n ?
If P(11, r) = P (12, r − 1) find r.
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.
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 letters E, K, S and V, one in each, were purchased from a plastic warehouse. How many ordered pairs of letters, to be used as initials, can be formed from them?
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 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 'FAILURE' be arranged so that the consonants may occupy only odd positions?
How many different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:
the vowels are always together?
How many permutations can be formed by the letters of the word, 'VOWELS', when
each word begins with E?
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 4 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 at a time.
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:
EXERCISES
In how many ways can the letters of the word 'ALGEBRA' be arranged without changing the relative order of the vowels and consonants?
How many words can be formed with the letters of the word 'UNIVERSITY', the vowels remaining together?
How many words can be formed by arranging the letters of the word 'MUMBAI' so that all M's come together?
Find the number of numbers, greater than a million, that can be formed with the digits 2, 3, 0, 3, 4, 2, 3.
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 letters of the word 'MOTHER' are written in all possible orders and these words are written out as in a dictionary, find the rank of the word 'MOTHER'.
Find the total number of ways in which six ‘+’ and four ‘−’ signs can be arranged in a line such that no two ‘−’ signs occur together.
In how many ways can the letters of the word
"INTERMEDIATE" be arranged so that:the vowels always occupy even places?
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
Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:
nCr + 2 · nCr − 1 + nCr − 2 = n + 2Cr.
There are 10 persons named\[P_1 , P_2 , P_3 , . . . . , P_{10}\]
Out of 10 persons, 5 persons are to be arranged in a line such that in each arrangement P1 must occur whereas P4 and P5 do not occur. Find the number of such possible arrangements.
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.
Find the number of permutations of n different things taken r at a time such that two specified things occur together?
If 35Cn +7 = 35C4n − 2 , then write the values of n.
