Advertisements
Advertisements
Question
If the letters of the word GARDEN are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, then find the ranks of the words
GARDEN
Advertisements
Solution
The letters of the word arranged in the dictionary order is A, D, E, G, N, R
Total number of letters = 6
The number of words begins with A = 5!
The number of words begins with D = 5!
The number of words begins with E = 5!
The number of words beginning with G = 5!
(But one of these words is GARDEN)
The number of words beginning with GAD = 3!
The number of words beginning with GAE = 3!
The number of words beginning with GAN = 3!
There are 3 ! words beginning with GAR one of these words is GARDEN.
The first word beginning with GAR is the word GARDEN.
∴ The rank of the word GARDEN 3 × 120 + 3 × 6 + 1 = 360 + 18 + 1 = 379
APPEARS IN
RELATED QUESTIONS
Compute `(8!)/(6! xx 2!)`
How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?
From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person cannot hold more than one position?
Which of the following are true:
(2 +3)! = 2! + 3!
How many three digit numbers can be formed by using the digits 0, 1, 3, 5, 7 while each digit may be repeated any number of times?
Write the number of ways in which 7 men and 7 women can sit on a round table such that no two women sit together ?
The number of ways in which the letters of the word 'CONSTANT' can be arranged without changing the relative positions of the vowels and consonants is
In a room there are 12 bulbs of the same wattage, each having a separate switch. The number of ways to light the room with different amounts of illumination is
How many 6-digit telephone numbers can be constructed with the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 if each numbers starts with 35 and no digit appear more than once?
Evaluate the following.
`(3! + 1!)/(2^2!)`
Three men have 4 coats, 5 waist coats and 6 caps. In how many ways can they wear them?
In how many ways 4 mathematics books, 3 physics books, 2 chemistry books and 1 biology book can be arranged on a shelf so that all books of the same subjects are together
Find the number of strings that can be made using all letters of the word THING. If these words are written as in a dictionary, what will be the 85th string?
Suppose m men and n women are to be seated in a row so that no two women sit together. If m > n, show that the number of ways in which they can be seated is `(m!(m + 1)!)/((m - n + 1)1)`
Ten different letters of alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have atleast one letter repeated is ______.
The number of signals that can be sent by 6 flags of different colours taking one or more at a time is ______.
A five-digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4 and 5 without repetitions. The total number of ways this can be done is ______.
The number of 5-digit telephone numbers having atleast one of their digits repeated is ______.
The number of words which can be formed out of the letters of the word ARTICLE, so that vowels occupy the even place is ______.
