Advertisements
Advertisements
प्रश्न
In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
Advertisements
उत्तर
A team of 3 boys and 3 girls is to be selected from 5 boys and 4 girls.
3 boys can be selected from 5 boys in `""^5C_3` ways.
3 girls can be selected from 4 girls in `""^4C_3 `ways.
Therefore, by multiplication principle, number of ways in which a team of 3 boys and 3 girls can be selected
= 5C3 x 4C3
= `(5!)/(3!2!) xx (4!)/(3!1!)`
= `(5 xx 4 xx 3!)/(3! xx 2) xx (4 xx 3!)/(3!)`
= 10 x 4 = 40
APPEARS IN
संबंधित प्रश्न
If nC8 = nC2, find nC2.
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.
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:
(i) exactly 3 girls?
(ii) atleast 3 girls?
(iii) atmost 3 girls?
Compute:
L.C.M. (6!, 7!, 8!)
From among the 36 teachers in a college, one principal, one vice-principal and the teacher-incharge are to be appointed. In how many ways can this be done?
How many three-digit numbers are there with no digit repeated?
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?
How many 3-digit numbers are there, with distinct digits, with each digit odd?
A number lock on a suitcase has 3 wheels each labelled with ten digits 0 to 9. If opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible? Also, find the number of unsuccessful attempts to open the lock.
If nC4 = nC6, find 12Cn.
If 15C3r = 15Cr + 3, find r.
If 2nC3 : nC2 = 44 : 3, find n.
In how many ways can a student choose 5 courses out of 9 courses if 2 courses are compulsory for every student?
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?
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
there is no restriction;
How many different selections of 4 books can be made from 10 different books, if
two particular books are always selected;
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?
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 (i) no girl?
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 the selection be made?
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: 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
How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?
How many words can be formed by taking 4 letters at a time from the letters of the word 'MORADABAD'?
There are 3 letters and 3 directed envelopes. Write the number of ways in which no letter is put in the correct envelope.
5C1 + 5C2 + 5C3 + 5C4 +5C5 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
There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two of them is
There are 13 players of cricket, out of which 4 are bowlers. In how many ways a team of eleven be selected from them so as to include at least two bowlers?
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
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.
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 ______.
A bag contains six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag if they can be of any colour
The value of `""^50"C"_4 + sum_("r" = 1)^6 ""^(56 - "r")"C"_3` is ______.
The number of numbers between 2,000 and 5,000 that can be formed with the digits 0, 1, 2, 3, 4, (repetition of digits is not allowed) and are multiple of 3 is?
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 ______.
