Advertisements
Advertisements
प्रश्न
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'?
Advertisements
उत्तर
In a dictionary, the words are arranged in alphabetical order. Therefore, in the given problem, we must consider the words beginning with E, H, I, N, T and Z.
∴ Number of words starting with E = 5! = 120
Number of words starting with H = 5! = 120
Number of words starting with I = 5! = 120
Number of words starting with N = 5! = 120
Number of words starting with T = 5! = 120
Now, the word will start with the letter Z.
After Z, alphabetically, the next letter would be E, which is as per the requirement of the word ZENITH.
After ZE, alphabetically, the next letter would be H, i.e. ZEH. The remaining three letters can be arranged in 3! ways.
Now, the next letter would be I, i.e. ZEI. The remaining three letters can be arranged in 3! ways.
Now, the next letter would be N, which as per the requirement of the word ZENITH.
After ZEN, alphabetically, the next letter would be H, i.e. ZENH. The remaining two letters can be arranged in 2! ways.
The next letter would now be I, i.e. ZENI, which is as per the requirement of the word ZENITH.
H will come after ZENI, which would be followed by T.
The word formed is ZENIHT.
The next word would be ZENITH.
Total number of intermediate words = 5\[\times\]120 + 3! + 3! + 2! + 1 + 1 = 616
APPEARS IN
संबंधित प्रश्न
Convert the following products into factorials:
(n + 1) (n + 2) (n + 3) ... (2n)
If (n + 1)! = 90 [(n − 1)!], find n.
If (n + 3)! = 56 [(n + 1)!], find n.
Prove that:
If P (5, r) = P (6, r − 1), find r ?
If P (9, r) = 3024, find r.
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?
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?
In how many ways can the letters of the word 'STRANGE' be arranged so that
the vowels never come together?
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 vowels come together?
How many words can be formed out of the letters of the word 'ARTICLE', so that vowels occupy even places?
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 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?
Find the number of words formed by permuting all the letters of the following words:
ARRANGE
Find the number of words formed by permuting all the letters of the following words:
INDIA
How many different numbers, greater than 50000 can be formed with the digits 0, 1, 1, 5, 9.
How many words can be formed from the letters of the word 'SERIES' which start with S and end with S?
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?
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S's are 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:
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.
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
Find the number of permutations of n different things taken r at a time such that two specified things occur together?
Write the expression nCr +1 + nCr − 1 + 2 × nCr in the simplest form.
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 12 boys may be divided into three groups of 4 boys each.
