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 15C4
Find the value of `""^80"C"_2`
Find the value of `""^20"C"_16 - ""^19"C"_16`
If `""^"n""C"_("r" - 1)` = 6435, `""^"n""C"_"r"` = 5005, `""^"n""C"_("r" + 1)` = 3003, find `""^"r""C"_5`.
If 20 points are marked on a circle, how many chords can be drawn?
Find the number of diagonals of an n-shaded polygon. In particular, find the number of diagonals when: n = 15
Ten points are plotted on a plane. Find the number of straight lines obtained by joining these points if no three points are collinear.
Ten points are plotted on a plane. Find the number of straight lines obtained by joining these points if four points are collinear.
Find n if `""^"n""C"_8 = ""^"n""C"_12`
Find n, if `""^(2"n")"C"_("r" - 1) = ""^(2"n")"C"_("r" + 1)`
find the value of `sum_("r" = 1)^4 ""^(21 - "r")"C"_4 + ""^17"C"_5`
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`
Five students are selected from 11. How many ways can these students be selected if two specified students are selected?
Find n if nCn–3 = 84
Find n and r if nPr = 720 and nCn–r = 120
Find the number of diagonals of an n-sided polygon. In particular, find the number of diagonals when n = 15
Find the number of diagonals of an n-sided polygon. In particular, find the number of diagonals when n = 8
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
Ten points are plotted on a plane. Find the number of straight lines obtained by joining these points if no three points are collinear
Ten points are plotted on a plane. Find the number of straight lines obtained by joining these points if four points are collinear
Find the number of triangles formed by joining 12 points if no three 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 nC8 = nC12
Find n if nCn–2 = 15
Find the differences between the greatest values in the following:
13Cr and 8Cr
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.
A question paper has two parts, A and B, each containing 10 questions. If a student has to choose 8 from part A and 5 from part B, In how many ways can he choose the questions?
Answer the following:
A student finds 7 books of his interest but can borrow only three books. He wants to borrow the Chemistry part-II book only if Chemistry Part-I can also be borrowed. Find the number of ways he can choose three books that he wants to borrow.
Answer the following:
Four parallel lines intersect another set of five parallel lines. Find the number of distinct parallelograms formed
The maximum value of z = 9x + 11y subject to 3x + 2y ≤ 12, 2x + 3y ≤ 12, x ≥ 0, y ≥ 0 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 ______.
