Question:
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
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
Updated On: Jun 14, 2022
- 55
- 66
- 77
- 88
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The Correct Option is C
Solution and Explanation
There are two possible cases Case I Five l 's, one 2's, one 3's
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
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
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Concepts Used:
Combinations
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Use of Combinations:
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