Advertisements
Advertisements
प्रश्न
A group consists of 9 men and 6 women. A team of 6 is to be selected. How many of possible selections will have at least 3 women?
उत्तर
There are 9 men and 6 women.
A team of 6 persons is to be formed such that it consists of at least 3 women.
Consider the following table:
| Case I |
Case II |
Case III |
Case IV |
|
| 3W 3M |
4W 2M |
5W 1M |
6W – |
|
| Number of ways | 6C3 × 9C3 = 20 × 84 = 1680 |
6C4 × 9C2 = 15 × 36 = 540 |
6C5 × 9C1 = 6 × 9 = 54 |
1 |
∴ No. of ways this can be done
= 1680 + 540 + 54 + 1
= 2275
∴ 2275 teams can be formed if the team consists of at least 3 women.
APPEARS IN
संबंधित प्रश्न
Find the value of `""^80"C"_2`
Find n if `""^"n""C"_("n" - 3)` = 84
Find n and r if `""^"n""C"_("r" - 1): ""^"n""C"_"r": ""^"n""C"_("r" + 1)` = 20:35:42
Find the number of ways of selecting a team of 3 boys and 2 girls from 6 boys and 4 girls.
After a meeting, every participant shakes hands with every other participants. If the number of handshakes is 66, find the number of participants in the meeting.
Find the number of diagonals of an n-shaded polygon. In particular, find the number of diagonals when: n = 10
Ten points are plotted on a plane. Find the number of straight lines obtained by joining these points if no three points are collinear.
Find the number of triangles formed by joining 12 points if four points are collinear.
Find n, if `""^21"C"_(6"n") = ""^21"C"_(("n"^2 + 5)`
Find n, if `""^"n""C"_("n" - 2)` = 15
Find the differences between the largest values in the following: `""^14"C"_r "and" ""^12"C"_r`
Find the differences between the largest values in the following: `""^13"C"_r "and" ""^8"C"_r`
A committee of 10 persons is to be formed from a group of 10 women and 8 men. How many possible committees will have at least 5 women? How many possible committees will have men in the majority?
A question paper has two sections. section I has 5 questions and section II has 6 questions. A student must answer at least two questions from each section among 6 questions he answers. How many different choices does the student have in choosing questions?
Five students are selected from 11. How many ways can these students be selected if two specified students are selected?
Find n if 2nC3 : nC2 = 52 : 3
Find r if 14C2r : 10C2r–4 = 143 : 10
If nCr–1 = 6435, nCr = 5005, nCr+1 = 3003, find rC5
Find the number of diagonals of an n-sided polygon. In particular, find the number of diagonals when n = 10
Find the number of diagonals of an n-sided polygon. In particular, find the number of diagonals when n = 15
Find the number of triangles formed by joining 12 points if no three points are collinear
Find the number of triangles formed by joining 12 points if four points are collinear
A word has 8 consonants and 3 vowels. How many distinct words can be formed if 4 consonants and 2 vowels are chosen?
Find n if 23C3n = 23C2n+3
Find n if 21C6n = `""^21"C"_(("n"^2 + 5))`
Find n if 2nCr–1 = 2nCr+1
Find the value of `sum_("r" = 1)^4 ""^((21 - "r"))"C"_4`
Find the differences between the greatest values in the following:
15Cr and 11Cr
In how many ways can a boy invite his 5 friends to a party so that at least three join the party?
A committee of 10 persons is to be formed from a group of 10 women and 8 men. How many possible committees will have at least 5 women? How many possible committees will have men in majority?
A question paper has two sections. section I has 5 questions and section II has 6 questions. A student must answer at least two question from each section among 6 questions he answers. How many different choices does the student have in choosing questions?
Five students are selected from 11. How many ways can these students be selected if two specified students are not selected?
Select the correct answer from the given alternatives.
The number of arrangements of the letters of the word BANANA in which two N's do not appear adjacently
Select the correct answer from the given alternatives.
The number of ways in which 5 male and 2 female members of a committee can be seated around a round table so that the two females are not seated together is
The maximum value of z = 9x + 11y subject to 3x + 2y ≤ 12, 2x + 3y ≤ 12, x ≥ 0, y ≥ 0 is _______.
If vertices of a parallelogram are respectively (2, 2), (3, 2), (4, 4), and (3, 4), then the angle between diagonals is ______
In how many ways can a group of 5 boys and 6 girls be formed out of 10 boys and 11 girls?
Out of 7 consonants and 4 vowels, the number of words (not necessarily meaningful) that can be made, each consisting of 3 consonants and 2 vowels, is ______.
