Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
Evaluate 8!
Find r if `""^5P_r = 2^6 P_(r-1)`
Find r if `""^5P_r = ""^6P_(r-1)`
A customer forgets a four-digits code for an Automatic Teller Machine (ATM) in a bank. However, he remembers that this code consists of digits 3, 5, 6 and 9. Find the largest possible number of trials necessary to obtain the correct code.
Find the number of ways in which one can post 5 letters in 7 letter boxes ?
Write the total number of possible outcomes in a throw of 3 dice in which at least one of the dice shows an even number.
The number of ways to arrange the letters of the word CHEESE are
A 5-digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways in which this can be done is
Find the number of arrangements that can be made out of the letters of the word “ASSASSINATION”.
The number of words with or without meaning that can be formed using letters of the word “EQUATION”, with no repetition of letters is:
A test consists of 10 multiple choice questions. In how many ways can the test be answered if question number n has n + 1 choices?
8 women and 6 men are standing in a line. How many arrangements are possible if any individual can stand in any position?
8 women and 6 men are standing in a line. In how many arrangements will all 6 men be standing next to one another?
If all permutations of the letters of the word AGAIN are arranged in the order as in a dictionary. What is the 49th word?
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 ______.
There are 10 persons named P1, P2, P3, ... P10. Out of 10 persons, 5 persons are to be arranged in a line such that in each arrangement P1 must occur whereas P4 and P5 do not occur. Find the number of such possible arrangements.
In the permutations of n things, r taken together, the number of permutations in which m particular things occur together is `""^(n - m)"P"_(r - m) xx ""^r"P"_m`.
The number of three-digit even numbers, formed by the digits 0, 1, 3, 4, 6, 7 if the repetition of digits is not allowed, is ______.
