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Vinod - IIT Bombay
🌐 India
If Amit picks up 10 and Anisha picks up 9 then
(10, 9, 1) (10, 9, 2) .... (10, 9, 8) - 8 ways
(10, 8, 1) (10, 8 2) ..... (10, 8, 7) - 7 ways
8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 8(9)/2 = 36
If Amit picks up 9 then
(9, 8, 1) ..... (9, 8, 7) ... = 7 ways
7 + 6 + 5 + 4 + 3 + 2 + 1 = 7(8)/2 = 28
For 8 - (6)(7)/2 = 21
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1 + 3 + 6 + 10 + 15 + 21 + 28 + 36
You either add them or apply the expression n(n+1)(n+2)/6,
sum of triangular numbers =8(9)(10)/6 = 120
Probability = 120/(10 x 9 x 8)=3/25
(10, 9, 1) (10, 9, 2) .... (10, 9, 8) - 8 ways
(10, 8, 1) (10, 8 2) ..... (10, 8, 7) - 7 ways
8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 8(9)/2 = 36
If Amit picks up 9 then
(9, 8, 1) ..... (9, 8, 7) ... = 7 ways
7 + 6 + 5 + 4 + 3 + 2 + 1 = 7(8)/2 = 28
For 8 - (6)(7)/2 = 21
.
.
1 + 3 + 6 + 10 + 15 + 21 + 28 + 36
You either add them or apply the expression n(n+1)(n+2)/6,
sum of triangular numbers =8(9)(10)/6 = 120
Probability = 120/(10 x 9 x 8)=3/25
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