Advertisements
Advertisements
प्रश्न
Find the number of words formed by permuting all the letters of the following words:
CONSTANTINOPLE
Advertisements
उत्तर
This word consists of 14 letters that include three Ns, two Os and two Ts.
The total number of words is the number of arrangements of 14 things, of which 3 are similar to one kind, 2 are similar to the second kind and 2 are similar to the third kind.
⇒\[\frac{14!}{3!2!2!} = \frac{14!}{24}\]
APPEARS IN
संबंधित प्रश्न
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 P (5, r) = P (6, r − 1), find r ?
If 5 P(4, n) = 6. P (5, n − 1), find n ?
If P (9, r) = 3024, find r.
If P (15, r − 1) : P (16, r − 2) = 3 : 4, find r.
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 three-digit numbers are there, with distinct digits, with each digit odd?
How many words, with or without meaning, can be formed by using all the letters of the word 'DELHI', using each letter exactly once?
How many words, with or without meaning, can be formed by using the letters of the word 'TRIANGLE'?
How many 3-digit even number can be made using the digits 1, 2, 3, 4, 5, 6, 7, if no digits is repeated?
How many permutations can be formed by the letters of the word, 'VOWELS', when
there is no restriction on letters?
How many permutations can be formed by the letters of the word, 'VOWELS', when
each word begins with E?
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?
Find the number of words formed by permuting all the letters of the following words:
INDIA
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 different signals can be made from 4 red, 2 white and 3 green flags by arranging all of them vertically on a flagstaff?
How many different numbers, greater than 50000 can be formed with the digits 0, 1, 1, 5, 9.
How many permutations of the letters of the word 'MADHUBANI' do not begin with M but end with I?
How many different arrangements can be made by using all the letters in the word 'MATHEMATICS'. How many of them begin with C? How many of them begin with T?
A biologist studying the genetic code is interested to know the number of possible arrangements of 12 molecules in a chain. The chain contains 4 different molecules represented by the initials A (for Adenine), C (for Cytosine), G (for Guanine) and T (for Thymine) and 3 molecules of each kind. How many different such arrangements are possible?
How many numbers greater than 1000000 can be formed by using the digits 1, 2, 0, 2, 4, 2, 4?
Find the total number of permutations of the letters of the word 'INSTITUTE'.
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 relative order of vowels and consonants do not alter?
Evaluate
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:
nCr + 2 · nCr − 1 + nCr − 2 = n + 2Cr.
How many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?
Write the number of ways in which 12 boys may be divided into three groups of 4 boys each.
