Advertisements
Advertisements
प्रश्न
Find the number of different words that can be formed from the letters of the word ‘TRIANGLE’ so that no vowels are together
Advertisements
उत्तर
Total number of words in ‘TRIANGLE’ = 8
Out of 5 are consonants and 3 are vowels
If vowels are not together, taken we have the following arrangement
V | C | V | C | V | C | V | C | V | C | V
Consonant can be arranged in 5! = 120 ways
Vowel occupy 6 places
∴ 3 vowels can be arranged in 6 places = 6P3
= `(6!)/((6 - 3)!)`
= `(6!)/(3!)`
= 120 ways
So, the total arrangement = 120 × 120 = 14400 ways
Here, the required arrangement = 14400 ways.
APPEARS IN
संबंधित प्रश्न
Evaluate 4! – 3!
Compute `(8!)/(6! xx 2!)`
if `1/(6!) + 1/(7!) = x/(8!)`, find x
Find n if n – 1P3 : nP4 = 1 : 9
How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?
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:
A coin is tossed three times and the outcomes are recorded. How many possible outcomes are there? How many possible outcomes if the coin is tossed four times? Five times? n times?
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?
Find the number of ways in which one can post 5 letters in 7 letter boxes ?
Three dice are rolled. Find the number of possible outcomes in which at least one die shows 5 ?
The number of permutations of n different things taking r at a time when 3 particular things are to be included is
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 six letter words that can be formed using the letters of the word "ASSIST" in which S's alternate with other letters 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
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
If (n+2)! = 60[(n–1)!], find n
The number of words with or without meaning that can be formed using letters of the word “EQUATION”, with no repetition of letters is:
Three men have 4 coats, 5 waist coats and 6 caps. In how many ways can they wear them?
A test consists of 10 multiple choice questions. In how many ways can the test be answered if each question has four choices?
A student appears in an objective test which contain 5 multiple choice questions. Each question has four choices out of which one correct answer.
What is the maximum number of different answers can the students give?
How many strings can be formed from the letters of the word ARTICLE, so that vowels occupy the even places?
A coin is tossed 8 times, how many different sequences containing six heads and two tails are possible?
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
The number of arrangements of the letters of the word BANANA in which two N's do not appear adjacently is ______.
How many words can be formed with the letters of the word MANAGEMENT by rearranging them?
If all permutations of the letters of the word AGAIN are arranged in the order as in a dictionary. What is the 49th word?
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)`
Three married couples are to be seated in a row having six seats in a cinema hall. If spouses are to be seated next to each other, in how many ways can they be seated? Find also the number of ways of their seating if all the ladies sit together.
In a certain city, all telephone numbers have six digits, the first two digits always being 41 or 42 or 46 or 62 or 64. How many telephone numbers have all six digits distinct?
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 ______.
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 |
Let b1, b2, b3, b4 be a 4-element permutation with bi ∈ {1, 2, 3, .......,100} for 1 ≤ i ≤ 4 and bi ≠ bj for i ≠ j, such that either b1, b2, b3 are consecutive integers or b2, b3, b4 are consecutive integers. Then the number of such permutations b1, b2, b3, b4 is equal to ______.
The number of permutations by taking all letters and keeping the vowels of the word ‘COMBINE’ in the odd places is ______.
