Advertisements
Advertisements
प्रश्न
How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?
Advertisements
उत्तर
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
संबंधित प्रश्न
The English alphabet has 5 vowels and 21 consonants. How many words with two different vowels and 2 different consonants can be formed from the alphabet?
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?
In a class there are 27 boys and 14 girls. The teacher wants to select 1 boy and 1 girl to represent the class in a function. In how many ways can the teacher make this selection?
How many four-digit numbers can be formed with the digits 3, 5, 7, 8, 9 which are greater than 7000, if repetition of digits is not allowed?
How many 9-digit numbers of different digits can be formed?
How many different numbers of six digits can be formed from the digits 3, 1, 7, 0, 9, 5 when repetition of digits is not allowed?
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?
If nC12 = nC5, find the value of n.
If 18Cx = 18Cx + 2, find x.
In how many ways can a football team of 11 players be selected from 16 players? How many of these will
include 2 particular players?
How many different products can be obtained by multiplying two or more of the numbers 3, 5, 7, 11 (without repetition)?
How many different selections of 4 books can be made from 10 different books, if
two particular books are always selected;
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(iii) at least 3 girls?
Determine the number of 5 cards combinations out of a deck of 52 cards if at least one of the 5 cards has to be a king?
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 parallelogram is cut by two sets of m lines parallel to its sides. Find the number of parallelograms thus formed.
Find the number of ways in which : (a) a selection
Write \[\sum^m_{r = 0} \ ^{n + r}{}{C}_r\] in the simplified form.
Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to
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
Given 11 points, of which 5 lie on one circle, other than these 5, no 4 lie on one circle. Then the number of circles that can be drawn so that each contains at least 3 of the given points is
If n + 1C3 = 2 · nC2 , then n =
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is
Find n if `""^6"P"_2 = "n" ""^6"C"_2`
Find n and r if `""^"n""P"_"r"` = 720 and `""^"n""C"_("n" - "r")` = 120
Ten students are to be selected for a project from a class of 30 students. There are 4 students who want to be together either in the project or not in the project. Find the number of possible selections.
Find the value of 15C4
In how many ways can the letters of the word 'IMAGE' be arranged so that the vowels should always occupy odd places?
A student has to answer 10 questions, choosing atleast 4 from each of Parts A and B. If there are 6 questions in Part A and 7 in Part B, in how many ways can the student choose 10 questions?
The straight lines l1, l2 and l3 are parallel and lie in the same plane. A total numbers of m points are taken on l1; n points on l2, k points on l3. The maximum number of triangles formed with vertices at these points are ______.
How many committee of five persons with a chairperson can be selected from 12 persons.
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 ______.
There are 12 points in a plane of which 5 points are collinear, then the number of lines obtained by joining these points in pairs is 12C2 – 5C2.
There are 10 professors and 20 lecturers out of whom a committee of 2 professors and 3 lecturer is to be formed. Find:
| C1 | C2 |
| (a) In how many ways committee: can be formed | (i) 10C2 × 19C3 |
| (b) In how many ways a particular: professor is included | (ii) 10C2 × 19C2 |
| (c) In how many ways a particular: lecturer is included | (iii) 9C1 × 20C3 |
| (d) In how many ways a particular: lecturer is excluded | (iv) 10C2 × 20C3 |
All possible numbers are formed using the digits 1, 1, 2, 2, 2, 2, 3, 4, 4 taken all at a time. The number of such numbers in which the odd digits occupy even places 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 ______.
A regular polygon has 20 sides. The number of triangles that can be drawn by using the vertices but not using the sides is
