Advertisements
Advertisements
Question
Find the number of words formed by permuting all the letters of the following words:
SERIES
Solution
This word consists of 6 letters that include two Ss and two Es.
The total number of words is the number of arrangements of 6 things, of which 2 are similar to one kind and 2 are similar to the second kind.
⇒\[\frac{6!}{2!2!}\]= 180
APPEARS IN
RELATED QUESTIONS
Convert the following products into factorials:
3 · 6 · 9 · 12 · 15 · 18
If (n + 3)! = 56 [(n + 1)!], find n.
If \[\frac{(2n)!}{3! (2n - 3)!}\] and \[\frac{n!}{2! (n - 2)!}\] are in the ratio 44 : 3, find n.
Prove that:
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 (n, 5) = 20. P(n, 3), find n ?
If P (n, 4) = 12 . P (n, 2), find n.
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.
In how many ways can five children stand in a queue?
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?
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 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.
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 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
all consonants come together?
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 all letters are used at a time.
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:
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 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 permutations of the letters of the word 'MADHUBANI' do not begin with M but end with I?
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?
The letters of the word 'SURITI' are written in all possible orders and these words are written out as in a dictionary. Find the rank of the word 'SURITI'.
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 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
Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:
Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.
Write the number of diagonals of an n-sided polygon.
Write the expression nCr +1 + nCr − 1 + 2 × nCr in the simplest form.