Question:
The value of $\,^{16}C_9 + \,^{16}C_{10} -\,^{16}C_6 -\,^{16}C_7$ is
The value of $\,^{16}C_9 + \,^{16}C_{10} -\,^{16}C_6 -\,^{16}C_7$ is
Updated On: Oct 24, 2025
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- $^{17}C_{10}$
- $^{17}C_3$
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The Correct Option is A
Solution and Explanation
${ }^{16} C _{9}+{ }^{16} C _{10^{-}}{ }^{16} C _{6^{-}}{ }^{16} C _{7}$
$={ }^{16} C _{9}+{ }^{16} C _{10^{-}}{ }^{16} C _{10^{-}}{ }^{16} C _{9}=0$
$\left(\because{ }^{ n } C _{ r }={ }^{ n } C _{( n - r )}\right)$
$={ }^{16} C _{9}+{ }^{16} C _{10^{-}}{ }^{16} C _{10^{-}}{ }^{16} C _{9}=0$
$\left(\because{ }^{ n } C _{ r }={ }^{ n } C _{( n - r )}\right)$
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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).