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 :
- 1120
- 1240
- 1880
- 1960
The Correct Option is B
Solution and Explanation
$= 15 \times 15 = (15)^2$
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
$= \left(15\right)^{2}+\left(14\right)^{2}+....+ \left(1\right)^{2}$
$= \frac{15\times16\times31}{6} = 1240$
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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).