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: atmost 3 girls?
Advertisements
उत्तर
If maximum 3 girls are to be included in the committee, then the committees will be formed as follows:
- No girls and 7 boys
- 1 girl and 6 boys
- 2 girls and 5 boys
- 3 girls and 4 boys
Hence, the total committees formed = 4C0 x 9C7 + 4C1 x 9C6 + 4C2 x 9C5 + 4C3 x 9C4
= 1 x 9C2 + 4C1 x 9C3 + 4C2 x 9C4 + 4C1 x 9C4
= 1 x `(9 xx 8)/(1 xx 2) + 4/1 xx (9 xx 8 xx 7)/(1 xx 2 xx 3) + (4 xx 3)/(1 xx 7) xx (9 xx 8 xx 7 xx 6)/(1 xx 2 xx 3 xx 4) + 4/1 xx (9 xx 8 xx 7 xx 6)/(1 xx 2 xx 3 xx 4)`
= 1 x 36 + 4 x 84 + 6 x 126 + 4 x 126
= 36 + 336 + 126 x (6+ 4)
= 372 + 1260
= 1632
APPEARS IN
संबंधित 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:
(i) exactly 3 girls?
(ii) atleast 3 girls?
(iii) atmost 3 girls?
Compute:
(i)\[\frac{30!}{28!}\]
How many A.P.'s with 10 terms are there whose first term is in the set {1, 2, 3} and whose common difference is in the set {1, 2, 3, 4, 5}?
How many three-digit numbers are there?
How many three-digit odd numbers are there?
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,
How many different five-digit number licence plates can be made if
the first-digit cannot be zero, but the repetition of digits is allowed?
Evaluate the following:
n + 1Cn
If nC12 = nC5, find the value of n.
f 24Cx = 24C2x + 3, find x.
If n +2C8 : n − 2P4 = 57 : 16, find n.
If nC4 , nC5 and nC6 are in A.P., then 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?
How many different selections of 4 books can be made from 10 different books, if
there is no restriction;
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?
Find the number of diagonals of (ii) a polygon of 16 sides.
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 (ii) triangles
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 how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?
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 20Cr + 1 = 20Cr − 1 , then r is equal to
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?
If α = mC2, then αC2 is equal to.
In how many ways can the letters of the word 'IMAGE' be arranged so that the vowels should always occupy odd places?
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 from the lot.
If 20 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, in how many points will they intersect each other?
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.
The number of triangles that are formed by choosing the vertices from a set of 12 points, seven of which lie on the same line is ______.
15C8 + 15C9 – 15C6 – 15C7 = ______.
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 value of `""^50"C"_4 + sum_("r" = 1)^6 ""^(56 - "r")"C"_3` 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 ______.
