Advertisements
Advertisements
प्रश्न
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?
उत्तर
The given word is THING
Arranging the letters of the word in the dictionary order
We have G, H, I, N, T
The number of strings that can be made using all the letters T, H, I, N, G of the word
THING is = 5! = 120
The number of words beginning with G = 4!
The number of words beginning with H = 4!
The number of words beginning with I = 4!
Number of words so far formed = 4! + 4! + 4!
= 24 + 24 + 24
= 72 words
As the required word is in the 85th position
The required word must begin with N
Number of words beginning with NG = 3!
A number of words beginning with NH = 3!
Total number of words so far formed
= 72 + 3! + 3!
= 72 + 6 + 6
= 84 words
The next string is the required string.
It should begin with NI and its first word beginning with NI which is NIGHT
∴ 85th strings are NIGHT.
APPEARS IN
संबंधित प्रश्न
Evaluate `(n!)/((n-r)!)` when n = 6, r = 2
How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?
Find r if `""^5P_r = 2^6 P_(r-1)`
Find x in each of the following:
Which of the following are true:
(2 × 3)! = 2! × 3!
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.
There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated ?
Write the number of ways in which 6 men and 5 women can dine at a round table if no two women sit together ?
Write the number of ways in which 5 boys and 3 girls can be seated in a row so that each girl is between 2 boys ?
The number of words from the letters of the word 'BHARAT' in which B and H will never come together, is
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
How many five digits telephone numbers can be constructed using the digits 0 to 9 If each number starts with 67 with no digit appears more than once?
In how many ways 5 boys and 3 girls can be seated in a row, so that no two girls are together?
Evaluate the following.
`((3!)! xx 2!)/(5!)`
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 of these 6-digit numbers are divisible by 4?
Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.
The number of words which can be formed out of the letters of the word ARTICLE, so that vowels occupy the even place is ______.
How many words (with or without dictionary meaning) can be made from the letters of the word MONDAY, assuming that no letter is repeated, if
| C1 | C2 |
| (a) 4 letters are used at a time | (i) 720 |
| (b) All letters are used at a time | (ii) 240 |
| (c) All letters are used but the first is a vowel | (iii) 360 |
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 ______.
The number of permutations by taking all letters and keeping the vowels of the word ‘COMBINE’ in the odd places is ______.
