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
How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?
Find x in each of the following:
How many 5-digit telephone numbers can be constructed using the digits 0 to 9. If each number starts with 67 and no digit appears more than once?
In how many ways can 4 letters be posted in 5 letter boxes?
Write the number of words that can be formed out of the letters of the word 'COMMITTEE' ?
The number of words that can be formed out of the letters of the word "ARTICLE" so that vowels occupy even places is
The number of ways to arrange the letters of the word CHEESE are
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
In how many ways 5 boys and 3 girls can be seated in a row, so that no two girls are together?
Find the number of arrangements that can be made out of the letters of the word “ASSASSINATION”.
A test consists of 10 multiple choice questions. In how many ways can the test be answered if each question has four choices?
Find the distinct permutations of the letters of the word MISSISSIPPI?
A coin is tossed 8 times, how many different sequences containing six heads and two tails are possible?
How many strings are there using the letters of the word INTERMEDIATE, if all the vowels are together
Each of the digits 1, 1, 2, 3, 3 and 4 is written on a separate card. The six cards are then laid out in a row to form a 6-digit number. How many distinct 6-digit numbers are there?
The number of arrangements of the letters of the word BANANA in which two N's do not appear adjacently is ______.
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 ______.
Find the number of different words that can be formed from the letters of the word ‘TRIANGLE’ so that no vowels are together
The number of permutations of n different objects, taken r at a line, when repetitions are allowed, is ______.
If the letters of the word 'MOTHER' be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word 'MOTHER' is ______.
