Advertisements
Advertisements
Question
How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?
Advertisements
Solution
2 out of 5 vowels and 3 out of 17 consonants can be chosen in \[{}^5 C_2 \times {}^{17} C_3\] ways.
Thus, there are \[{}^5 C_2 \times {}^{17} C_3\]groups, each containing 2 vowels and 3 consonants.
Each group contains 5 letters, which can be arranged in
APPEARS IN
RELATED QUESTIONS
Determine n if `""^(2n)C_3 : ""^nC_3 = 11: 1`
How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?
From Goa to Bombay there are two roots; air, and sea. From Bombay to Delhi there are three routes; air, rail and road. From Goa to Delhi via Bombay, how many kinds of routes are there?
A coin is tossed five times and outcomes are recorded. How many possible outcomes are there?
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?
There are 5 books on Mathematics and 6 books on Physics in a book shop. In how many ways can a students buy : (i) a Mathematics book and a Physics book (ii) either a Mathematics book or a Physics book?
How many different five-digit number licence plates can be made if
first digit cannot be zero and the repetition of digits is not 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`
How many 9-digit numbers of different digits can be formed?
If nC10 = nC12, find 23Cn.
If n +2C8 : n − 2P4 = 57 : 16, find n.
If 28C2r : 24C2r − 4 = 225 : 11, find r.
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.
How many different selections of 4 books can be made from 10 different books, if
two particular books are always selected;
In how many ways can a committee of 5 persons be formed out of 6 men and 4 women when at least one woman has to be necessarily selected?
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: atmost 3 girls?
Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many (i) straight lines
Find the number of ways in which : (b) an arrangement, of four letters can be made from the letters of the word 'PROPORTION'.
If C (n, 12) = C (n, 8), then C (22, n) is equal to
If\[\ ^{( a^2 - a)}{}{C}_2 = \ ^{( a^2 - a)}{}{C}_4\] , then a =
5C1 + 5C2 + 5C3 + 5C4 +5C5 is equal to
In how many ways can a committee of 5 be made out of 6 men and 4 women containing at least one women?
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
How many different committees of 5 can be formed from 6 men and 4 women on which exact 3 men and 2 women serve?
(a) 6
(b) 20
(c) 60
(d) 120
The number of diagonals that can be drawn by joining the vertices of an octagon is
Find n if `""^6"P"_2 = "n" ""^6"C"_2`
There are 3 wicketkeepers and 5 bowlers among 22 cricket players. A team of 11 players is to be selected so that there is exactly one wicketkeeper and at least 4 bowlers in the team. How many different teams can be formed?
Find the value of 15C4
Find the value of 80C2
Find the value of 20C16 – 19C16
In how many ways can the letters of the word 'IMAGE' be arranged so that the vowels should always occupy odd places?
A box contains two white, three black and four red balls. In how many ways can three balls be drawn from the box, if atleast one black ball is to be included in the draw
A convex polygon has 44 diagonals. Find the number of its sides.
Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to ______.
In a football championship, 153 matches were played, Every two teams played one match with each other. The number of teams, participating in the championship is ______.
The total number of ways in which six ‘+’ and four ‘–’ signs can be arranged in a line such that no two signs ‘–’ occur together 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.
There are 12 balls numbered from 1 to 12. The number of ways in which they can be used to fill 8 places in a row so that the balls are with numbers in ascending or descending order is equal to ______.
The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word 'SYLLABUS' such that two letters are distinct and two letters are alike is ______.
