a, b, c are three positive integers (not necessarily distinct) that add up to give 11. How many such combinations of a, b and c exists? A.150 B.55 C.120 D.45

Asked by GeoffreyRichards | 22nd Nov, 2010, 08:32: AM

Expert Answer:

Dear student,
 
a, b,and c are positive integers so they take values 1,2,3-------9
Once we select a and b then c is fixed as 11-(a+b)
We thus have to select a and b.
 
let
a = 1 so b = 1,2--------9. The number of ways = 1 x 9 = 9.
a = 2 so b = 1,2--------8. The number of ways = 1 x 8 = 8.
a = 3 so b = 1,2--------7. The number of ways = 1 x 7 = 7.
a = 4 so b = 1,2--------6. The number of ways = 1 x 6 = 6.
a = 5 so b = 1,2--------5. The number of ways = 1 x 5 = 5.
a = 6 so b = 1,2--------4. The number of ways = 1 x 4 = 4.
a = 7 so b = 1,23.            The number of ways = 1 x 3 = 3.
a = 8 so b = 1,2 .             The number of ways = 1 x 2 = 2.
a = 9 so b = 1.                The number of ways = 1 x 1 = 1.
 
The total number of ways is = 1+2+3--------+9 = 45
 
 
We hope this clarifies your query,
regards,
Team Topper Learning

Answered by  | 1st Dec, 2010, 10:40: AM

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