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Total of Rs 83 is to be given a way in terms of 2 rupees, 3 rupee and 5 rupee coins so that coin of each kind is present and the number of 2 rupee coins is less than the number of 3 rupee coins which less than the number of 5 rupee coins the number of different ways of giving away the coins is $l$ then $l - 2$ equal to

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answer is 8.

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Detailed Solution

$2 x + 3 y + 5 z = 83, x > 0, y > 0, z > 0' x < y < z$

put $x = x_{1} + 1, x_{1} > 0, y = x_{2} + x + 1 = x_{1} + x_{2} + 2$ $x \geq 0$

$z = x_{3} + 1 + y = x_{1} + x_{2} + x_{3} + 3, x_{3} \geq 0$

$10 x_{1} + 8 x_{2} + 5 x_{3} = 60$

For non –negative integral solution is 10

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