Question:
The number of ways of selecting $15$ teams from $15$ men and $15$ women, such that each team consists of a man and a woman. is :
The number of ways of selecting $15$ teams from $15$ men and $15$ women, such that each team consists of a man and a woman. is :
Updated On: Apr 28, 2025
- 1120
- 1240
- 1880
- 1960
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Number of ways of selecting a man and a woman for a team from 15 men and 15 women
$= 15 \times 15 = (15)^2$
Number of ways of selecting a man and a woman for next team out of the remaining 14 men and 14 women.
$= 14 \times 14 = (14)^2$ Similarly for other teams
Hence required number of ways
$= \left(15\right)^{2}+\left(14\right)^{2}+....+ \left(1\right)^{2}$
$= \frac{15\times16\times31}{6} = 1240$
$= 15 \times 15 = (15)^2$
Number of ways of selecting a man and a woman for next team out of the remaining 14 men and 14 women.
$= 14 \times 14 = (14)^2$ Similarly for other teams
Hence required number of ways
$= \left(15\right)^{2}+\left(14\right)^{2}+....+ \left(1\right)^{2}$
$= \frac{15\times16\times31}{6} = 1240$
Was this answer helpful?
0
0
Top Questions on Combinations
- The number of ways in which a committee of 7 members can be formed from 6 teachers, 5 fathers and 4 students in such a way that at least one from each group is included and teachers form the majority among them, is:
- AP EAPCET - 2025
- Mathematics
- Combinations
- A shop has 4 distinct flavors of ice-cream. One can purchase any number of scoops of any flavor. The order in which the scoops are purchased is inconsequential. If one wants to purchase 3 scoops of ice-cream, in how many ways can one make that purchase?
- A group of 9 students, s1, s2,…., s9, is to be divided to form three teams X, Y and Z of sizes 2, 3, and 4, respectively. Suppose that s1 cannot be selected for the team X and s2 cannot be selected for the team Y. Then the number of ways to form such teams, is _______.
- JEE Advanced - 2024
- Mathematics
- Combinations
- A committee of 11 members is to be formed out of 8 males and 5 females. If \( m \) is the number of ways the committee is formed with at least 6 males and \( n \) is the number of ways with at least 3 females, then:
- MHT CET - 2024
- Mathematics
- Combinations
- There are 15 points in a plane, no three of which are in a straight line, except 6, all of which are in a straight line. The number of straight lines which can be drawn by joining them is
- JKCET - 2024
- Mathematics
- Combinations
View More Questions
Questions Asked in JEE Main exam
- The variance of the numbers 8, 21, 34, 47, \dots, 320, is:
- JEE Main - 2025
- Arithmetic Progression and Variance
- Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : If Young’s double slit experiment is performed in an optically denser medium than air, then the consecutive fringes come closer.
Reason (R) : The speed of light reduces in an optically denser medium than air while its frequency does not change.
In the light of the above statements, choose the most appropriate answer from the options given below : - The increase in pressure required to decrease the volume of a water sample by 0.2percentage is \( P \times 10^5 \, \text{Nm}^{-2} \). Bulk modulus of water is \( 2.15 \times 10^9 \, \text{Nm}^{-2} \). The value of \( P \) is ________________.
- JEE Main - 2025
- System of Particles & Rotational Motion
The motion of an airplane is represented by the velocity-time graph as shown below. The distance covered by the airplane in the first 30.5 seconds is km.
- JEE Main - 2025
- Kinematics
- A force \( \mathbf{F} = 2\hat{i} + b\hat{j} + \hat{k} \) is applied on a particle and it undergoes a displacement \( \mathbf{r} = \hat{i} - 2\hat{j} - \hat{k} \). What will be the value of \( b \), if the work done on the particle is zero?
- JEE Main - 2025
- Work and Energy
View More Questions
Concepts Used:
Combinations
The method of forming subsets by selecting data from a larger set in a way that the selection order does not matter is called the combination.
- It means the combination of about ‘n’ things taken ‘k’ at a time without any repetition.
- The combination is used for a group of data where the order of data does not matter.
- For example, Imagine you go to a restaurant and order some soup.
- Five toppings can complement the soup, namely:
- croutons,
- orange zest,
- grated cheese,
- chopped herbs,
- fried noodles.
But you are only allowed to pick three.
- There can be several ways in which you can enhance your soup with savory.
- The selection of three toppings (subset) from the five toppings (larger set) is called a combination.
Use of Combinations:
It is used for a group of data (where the order of data doesn’t matter).