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
DANGER
उत्तर
The dictionary order of the letters of the given word is A, D, E, G, N, R
In the dictionary order of words which begin with A, comes first.
If we fill the first place with A, the remaining 5 letters can be arranged in 5! ways. Proceeding like this
Number of words beginning with D = 5! = 120
Number of words beginning with DAE = 3! = 6
Number of words beginning with DAG = 3! = 6
Number of words beginning with DANE = 2! = 2
Number of words beginning with DANGE = 1! = 1
(which is the word DANGER)
∴ The rank of the word DANGER = 120 + 6 + 6 + 2 + 1 = 135
APPEARS IN
संबंधित प्रश्न
Evaluate 4! – 3!
Evaluate `(n!)/((n-r)!)` when n = 6, r = 2
How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?
In how many ways can the letters of the word PERMUTATIONS be arranged if the there are always 4 letters between P and S?
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together?
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?
Write the number of arrangements of the letters of the word BANANA in which two N's come together.
If in a group of n distinct objects, the number of arrangements of 4 objects is 12 times the number of arrangements of 2 objects, then the number of objects is
The number of different ways in which 8 persons can stand in a row so that between two particular persons A and B there are always two persons, 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
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”.
Find the rank of the word ‘CHAT’ in the dictionary.
A test consists of 10 multiple choice questions. In how many ways can the test be answered if each question has four choices?
How many ways can the product a2 b3 c4 be expressed without exponents?
Choose the correct alternative:
The product of r consecutive positive integers is divisible b
Choose the correct alternative:
If Pr stands for rPr then the sum of the series 1 + P1 + 2P2 + 3P3 + · · · + nPn 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.
