Advertisements
Advertisements
प्रश्न
Find the number of words formed by permuting all the letters of the following words:
RUSSIA
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:
3 · 6 · 9 · 12 · 15 · 18
If (n + 2)! = 60 [(n − 1)!], find n.
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:
\[\frac{n!}{(n - r)! r!} + \frac{n!}{(n - r + 1)! (r - 1)!} = \frac{(n + 1)!}{r! (n - r + 1)!}\]
If P (5, r) = P (6, r − 1), find r ?
If nP4 = 360, find the value of 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.
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?
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 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?
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 occupy only the odd places?
How many different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:
the letter G always occupies the first place?
How many different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:
the letters P and I respectively occupy first and last place?
How many different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:
the vowels always occupy even places?
How many permutations can be formed by the letters of the word, 'VOWELS', when
each word begins with O and ends with L?
How many permutations can be formed by the letters of the word, 'VOWELS', when
all consonants come together?
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 but first is vowel.
Find the number of words formed by permuting all the letters of the following words:
INDIA
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 'ARRANGE' be arranged so that the two R's are never together?
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?
In how many ways can 4 red, 3 yellow and 2 green discs be arranged in a row if the discs of the same colour are indistinguishable?
Find the total number of permutations of the letters of the word 'INSTITUTE'.
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'.
If the permutations of a, b, c, d, e taken all together be written down in alphabetical order as in dictionary and numbered, find the rank of the permutation debac ?
Prove that the product of 2n consecutive negative integers is divisible by (2n)!
Evaluate
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.
How many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?
If 35Cn +7 = 35C4n − 2 , then write the values of n.
Write the number of ways in which 12 boys may be divided into three groups of 4 boys each.