Advertisements
Advertisements
प्रश्न
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?
Advertisements
उत्तर
A committee of 7 members is to be formed from 9 boys and 4 girls.
When there are 3 girls in that committee, then there will be 4 boys in that committee. Ways to choose 3 girls and 4 boys
= 4C3 x 9C4
= 4C1 x 9C4
[∵ 4C3 = 4C1]
= `4/1 xx (9 xx 8 xx 7 xx 6)/(1.2.3.4)`
= 9 x 8 x 7 = 504
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?
From a class of 25 students, 10 are to be chosen for an excursion party. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen?
Compute:
(i)\[\frac{30!}{28!}\]
Prove that
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?
There are 6 multiple choice questions in an examination. How many sequences of answers are possible, if the first three questions have 4 choices each and the next three have 2 each?
How many three-digit numbers are there?
If nC12 = nC5, find the value of n.
If 15Cr : 15Cr − 1 = 11 : 5, find r.
If n +2C8 : n − 2P4 = 57 : 16, 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 student is included.
How many triangles can be obtained by joining 12 points, five of which are collinear?
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?
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.
In how many ways can one select a cricket team of eleven from 17 players in which only 5 persons can bowl if each cricket team of 11 must include exactly 4 bowlers?
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?
If 15C3r = 15Cr + 3 , then r is equal to
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
In how many ways can a committee of 5 be made out of 6 men and 4 women containing at least one women?
If C0 + C1 + C2 + ... + Cn = 256, then 2nC2 is equal to
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 parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is
Find the value of 20C16 – 19C16
If α = mC2, then αC2 is equal to.
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 ______.
How many committee of five persons with a chairperson can be selected from 12 persons.
A convex polygon has 44 diagonals. Find the number of its sides.
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 no girls
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 one boy and one girl
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 ______.
15C8 + 15C9 – 15C6 – 15C7 = ______.
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 scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at least 2 Indians and double the number of foreigners as Indians. Then the number of ways, the committee can be formed is ______.
Number of selections of at least one letter from the letters of MATHEMATICS, is ______.
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 ______.
There are ten boys B1, B2, ...., B10 and five girls G1, G2, ...., G5 in a class. Then the number of ways of forming a group consisting of three boys and three girls, if both B1 and B2 together should not be the members of a group is ______.
