Advertisements
Advertisements
प्रश्न
All the letters of the word ‘EAMCOT’ are arranged in different possible ways. The number of such arrangements in which no two vowels are adjacent to each other is ______.
विकल्प
360
144
72
54
Advertisements
उत्तर
All the letters of the word ‘EAMCOT’ are arranged in different possible ways. The number of such arrangements in which no two vowels are adjacent to each other is 144.
Explanation:
We note that there are 3 consonants and 3 vowels E, A and O.
Since no two vowels have to be together, the possible choice for vowels are the places marked as ‘X’.
X M X C X T X, these vowels can be arranged in 4P3 ways 3 consonents can be arranged in 3 ways.
Hence, the required number of ways = 3! × 4P3 = 144.
APPEARS IN
संबंधित प्रश्न
If nC8 = nC2, find nC2.
How many chords can be drawn through 21 points on a circle?
How many 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7 and 9 which are divisible by 10 and no digit is repeated?
Compute:
(i)\[\frac{30!}{28!}\]
A letter lock consists of three rings each marked with 10 different letters. In how many ways it is possible to make an unsuccessful attempt to open the lock?
A team consists of 6 boys and 4 girls and other has 5 boys and 3 girls. How many single matches can be arranged between the two teams when a boy plays against a boy and a girl plays against a girl?
How many different five-digit number licence plates can be made if
the first-digit cannot be zero, but the repetition of digits is allowed?
Since the number has to be greater than 8000, the thousand's place can be filled by only two digits, i.e. 8 and 9.
Now, the hundred's place can be filled with the remaining 4 digits as the repetition of the digits is not allowed.
The ten's place can be filled with the remaining 3 digits.
The unit's place can be filled with the remaining 2 digits.
Total numbers that can be formed = `2xx4xx3xx2=48`
If 2nC3 : nC2 = 44 : 3, find n.
There are 10 professors and 20 students out of whom a committee of 2 professors and 3 students is to be formed. Find the number of ways in which this can be done. Further find in how many of these committees:
a particular professor is included.
From 4 officers and 8 jawans in how many ways can 6 be chosen. to include at least one officer?
In an examination, a student has to answer 4 questions out of 5 questions; questions 1 and 2 are however compulsory. Determine the number of ways in which the student can make the choice.
A candidate is required to answer 7 questions out of 12 questions which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. In how many ways can he choose the 7 questions?
Find the number of diagonals of (ii) a polygon of 16 sides.
A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of: exactly 3 girls?
In an examination, a question paper consists of 12 questions divided into two parts i.e., Part I and Part II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions?
A business man hosts a dinner to 21 guests. He is having 2 round tables which can accommodate 15 and 6 persons each. In how many ways can he arrange the guests?
There are 3 letters and 3 directed envelopes. Write the number of ways in which no letter is put in the correct envelope.
There are 12 points in a plane. The number of the straight lines joining any two of them when 3 of them are collinear, is
If C0 + C1 + C2 + ... + Cn = 256, then 2nC2 is equal to
The number of ways in which a host lady can invite for a party of 8 out of 12 people of whom two do not want to attend the party together is
If 43Cr − 6 = 43C3r + 1 , then the value of r is
The number of diagonals that can be drawn by joining the vertices of an octagon is
The value of\[\left( \ ^{7}{}{C}_0 + \ ^{7}{}{C}_1 \right) + \left( \ ^{7}{}{C}_1 + \ ^{7}{}{C}_2 \right) + . . . + \left( \ ^{7}{}{C}_6 + \ ^{7}{}{C}_7 \right)\] is
Find n and r if `""^"n""P"_"r"` = 720 and `""^"n""C"_("n" - "r")` = 120
There are 20 straight lines in a plane so that no two lines are parallel and no three lines are concurrent. Determine the number of points of intersection.
There are 8 doctors and 4 lawyers in a panel. Find the number of ways for selecting a team of 6 if at least one doctor must be in the team.
Find the value of 80C2
The value of `(""^9"C"_0 + ""^9"C"_1) + (""^9"C"_1 + ""^9"C"_2) + ... + (""^9"C"_8 + ""^9"C"_9)` is ______
A boy has 3 library tickets and 8 books of his interest in the library. Of these 8, he does not want to borrow Mathematics Part II, unless Mathematics Part I is also borrowed. In how many ways can he choose the three books to be borrowed?
We wish to select 6 persons from 8, but if the person A is chosen, then B must be chosen. In how many ways can selections be made?
In how many ways can a football team of 11 players be selected from 16 players? How many of them will exclude 2 particular players?
A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has at least three girls.
Given 5 different green dyes, four different blue dyes and three different red dyes, the number of combinations of dyes which can be chosen taking at least one green and one blue dye is ______.
A box contains 2 white balls, 3 black balls and 4 red balls. The number of ways three balls be drawn from the box if at least one black ball is to be included in the draw is ______.
A candidate is required to answer 7 questions out of 12 questions which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. He can choose the seven questions in 650 ways.
If number of arrangements of letters of the word "DHARAMSHALA" taken all at a time so that no two alike letters appear together is (4a.5b.6c.7d), (where a, b, c, d ∈ N), then a + b + c + d is equal to ______.
Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear is ______.
