# Quantitative Aptitude :: Permutation and Combination - Discussion

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## How many different integers can be expressed as the sum of three distinct numbers from the set {3, 10, 17, 24, 31, 38, 45, 52}?

A8

B56

C16

D15

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the smallest sum of three numbe is 3 10 17=30

and the largest sum of three number is 38 45 52=135

as we know that the series is in Ap so d=7(10-3)

so total number =(135-30)/7 =16

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In this question we are not asked how many ways we can select 3 numbers out of 8.

But how many different numbers can be expressed as a sum of three numbers from the given set.

For example, 3 + 10 + 31 = 3 + 17 + 24 = 47. So 47 can be expressed as a sum of 3 numbers in two different ways but 47 should be considered as only one number.

Now the minimum number that can be expressed as a sum of 3 numbers = 30. (3+10+17)

The next number is 37.

Similarly the largest number is 38 + 45 + 52 = 135.

So there exists many numbers in between, with common difference of 7.

Total numbers = (l?a)/d +1 = (135-30)/7 +1= 15+1=16.

But how many different numbers can be expressed as a sum of three numbers from the given set.

For example, 3 + 10 + 31 = 3 + 17 + 24 = 47. So 47 can be expressed as a sum of 3 numbers in two different ways but 47 should be considered as only one number.

Now the minimum number that can be expressed as a sum of 3 numbers = 30. (3+10+17)

The next number is 37.

Similarly the largest number is 38 + 45 + 52 = 135.

So there exists many numbers in between, with common difference of 7.

Total numbers = (l?a)/d +1 = (135-30)/7 +1= 15+1=16.

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