The number of seven-digit integers, with sum of the digits equal to $10$ and formed by using the digits $1, 2$ and $3$ only, is
- 55
- 66
- 77
- 88
The Correct Option is C
Solution and Explanation
Number of numbers = $\frac{7!}{5!}=42$ Case II Four l 's, three 2's
Number of numbers =$\frac{7!}{4!3!}=35$
$\therefore $ Total number of numbers = 42 + 35 = 77
Top Questions on Combinations
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Questions Asked in JEE Advanced exam
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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).