Advertisements
Advertisements
प्रश्न
Find the number of words formed by permuting all the letters of the following words:
RUSSIA
Advertisements
उत्तर
This word consists of 6 letters that include two Ss.
The total number of words is the number of arrangements of 6 things, of which 2 are similar to one kind.
⇒\[\frac{6!}{2!}\]= 360
APPEARS IN
संबंधित प्रश्न
Convert the following products into factorials:
1 · 3 · 5 · 7 · 9 ... (2n − 1)
If \[\frac{(2n)!}{3! (2n - 3)!}\] and \[\frac{n!}{2! (n - 2)!}\] are in the ratio 44 : 3, find n.
Prove that:
If 5 P(4, n) = 6. P (5, n − 1), find n ?
If P (9, r) = 3024, find r.
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 n +5Pn +1 =\[\frac{11 (n - 1)}{2}\]n +3Pn, find n.
How many three-digit numbers are there, with distinct digits, with each digit odd?
There are two works each of 3 volumes and two works each of 2 volumes; In how many ways can the 10 books be placed on a shelf so that the volumes of the same work are not separated?
How many three-digit numbers are there, with no digit repeated?
If a denotes the number of permutations of (x + 2) things taken all at a time, b the number of permutations of x things taken 11 at a time and c the number of permutations of x − 11 things taken all at a time such that a = 182 bc, find the value of x.
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?
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.
In how many ways can the letters of the word 'FAILURE' be arranged so that the consonants may occupy only odd positions?
In how many ways can the letters of the word 'STRANGE' be arranged so that
the vowels never 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 words can be formed out of the letters of the word, 'ORIENTAL', so that the vowels always occupy the odd places?
How many permutations can be formed by the letters of the word, 'VOWELS', when
all consonants come together?
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?
m men and n women are to be seated in a row so that no two women sit together. if m > n then show that the number of ways in which they can be seated as\[\frac{m! (m + 1)!}{(m - n + 1) !}\]
How many three letter words can be made using the letters of the word 'ORIENTAL'?
Find the number of words formed by permuting all the letters of the following words:
INDEPENDENCE
Find the number of words formed by permuting all the letters of the following words:
CONSTANTINOPLE
Find the total number of arrangements of the letters in the expression a3 b2 c4 when written at full length.
How many words can be formed by arranging the letters of the word 'MUMBAI' so that all M's 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?
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.
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.
In how many ways can the letters of the word
"INTERMEDIATE" be arranged so that:the vowels always occupy even places?
In how many ways can the letters of the word "INTERMEDIATE" be arranged so that:
the relative order of vowels and consonants do not alter?
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
Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.
Write the maximum number of points of intersection of 8 straight lines in a plane.
