Advertisements
Advertisements
प्रश्न
Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to
पर्याय
60
120
7200
none of these
Advertisements
उत्तर
7200
2 out of 4 vowels can be chosen in 4C2 ways and 3 out of 5 consonants can be chosen in 5C3 ways.
Thus, there are \[\left( C_2 \times {}^5 {C^4}_3 \right)\] groups, each containing 2 vowels and 3 consonants.
Each group contains 5 letters that can be arranged in 5! ways.
∴ Required number of words =\[\left( {}^4 C_2 \times {}^5 C_3 \right) \times 5! = 60 \times 120 = 7200\]
APPEARS IN
संबंधित प्रश्न
How many chords can be drawn through 21 points on a circle?
A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.
There are four parcels and five post-offices. In how many different ways can the parcels be sent by registered post?
How many four digit different numbers, greater than 5000 can be formed with the digits 1, 2, 5, 9, 0 when repetition of digits is not allowed?
Evaluate the following:
14C3
Evaluate the following:
35C35
Evaluate the following:
n + 1Cn
Evaluate the following:
If 15C3r = 15Cr + 3, 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 student is included.
How many different selections of 4 books can be made from 10 different books, if
two particular books are always selected;
In a village, there are 87 families of which 52 families have at most 2 children. In a rural development programme, 20 families are to be helped chosen for assistance, of which at least 18 families must have at most 2 children. In how many ways can the choice be made?
Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.
Determine the number of 5 cards combinations out of a deck of 52 cards if there is exactly one ace in each combination.
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?
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'.
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
Three persons enter a railway compartment. If there are 5 seats vacant, in how many ways can they take these seats?
There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two of them is
Find n if `""^6"P"_2 = "n" ""^6"C"_2`
Find the number of ways of dividing 20 objects in three groups of sizes 8, 7, and 5.
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.
In how many ways can a football team of 11 players be selected from 16 players? How many of them will include 2 particular players?
Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to ______.
Everybody in a room shakes hands with everybody else. The total number of handshakes is 66. The total number of persons in the room is ______.
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is ______.
The number of ways in which a team of eleven players can be selected from 22 players always including 2 of them and excluding 4 of them is ______.
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 ______.
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 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 ______.
The value of `""^50"C"_4 + sum_("r" = 1)^6 ""^(56 - "r")"C"_3` is ______.
There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are wicketkeepers. The number of ways, a team of 11 players be selected from them so as to include at least 4 bowlers, 5 batsmen and 1 wicketkeeper, is ______.
The number of positive integers satisfying the inequality `""^(n+1)C_(n-2) - ""^(n+1)C_(n-1) ≤ 100` is ______.
Number of selections of at least one letter from the letters of MATHEMATICS, is ______.
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 no. of different ways, the letters of the word KUMARI can be placed in the 8 boxes of the given figure so that no row remains empty will be ______.
