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 [2009]

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 [2009]

Smart Achievers · Accepted Answer

(3)

We have to form 7 digit numbers, using the digits 1, 2 and 3 only, such that the sum of the digits in a number = 10. This can be done by taking 2, 2, 2, 1, 1, 1, 1 or by taking 2, 3, 1, 1, 1, 1, 1.

$∴$ $Number of ways = \frac{7!}{3! 4!} + \frac{7!}{5!} = 77$

Solution

Q.
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 [2009]

1 55

2 66

3 77

4 88

Ans.
(3)

We have to form 7 digit numbers, using the digits 1, 2 and 3 only, such that the sum of the digits in a number = 10. This can be done by taking 2, 2, 2, 1, 1, 1, 1 or by taking 2, 3, 1, 1, 1, 1, 1.

$∴$ $Number of ways = \frac{7!}{3! 4!} + \frac{7!}{5!} = 77$

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