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?
Advertisements
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 the value of `""^20"C"_16 - ""^19"C"_16`
If `""^"n""P"_"r" = 1814400` and `""^"n""C"_"r"` = 45, find r.
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.
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 `""^23"C"_(3"n") = ""^23"C"_(2"n" + 3)`
Find n, if `""^(2"n")"C"_("r" - 1) = ""^(2"n")"C"_("r" + 1)`
Find r if `""^11"C"_4 + ""^11"C"_5 + ""^12"C"_6 + ""^13"C"_7 = ""^14"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?
Nine friends decide to go for a picnic in two groups. One group decides to go by car and the other group decides to go by train. Find the number of different ways of doing so if there must be at least 3 friends in each group.
Find n if nCn–3 = 84
Find n and r if nCr–1 : nCr : nCr+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.
If 20 points are marked on a circle, how many chords can be drawn?
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 = 12
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
Find n if 2nCr–1 = 2nCr+1
Find r if 11C4 + 11C5 + 12C6 + 13C7 = 14Cr
In how many ways can a boy invite his 5 friends to a party so that at least three join the party?
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?
Five students are selected from 11. How many ways can these students be selected if two specified students are 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?
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
Answer the following:
Find the number of ways of dividing 20 objects in three groups of sizes 8, 7 and 5
If `1/(8!) + 1/(7!) = x/(9!)`, than x is equal to ______.
If vertices of a parallelogram are respectively (2, 2), (3, 2), (4, 4), and (3, 4), then the angle between diagonals is ______
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 ______.
