# Confectionery

The village markets have 5 kinds of sweets, one weighs 31 grams. How many different ways a customer can buy 1.519 kg sweets.

Result

n =  292825

#### Solution:

$x = \dfrac{1000\cdot 1.519}{ 31}= 49 \ \\ \ \\ n = C_{{ 49}}(49+5-1) = \ \\ = C_{{ 49}}(53) = \dbinom{ 53}{ 49} = \dfrac{ 53! }{ 49!(53-49)!} = \dfrac{ 53 \cdot 52 \cdot 51 \cdot 50 } { 4 \cdot 3 \cdot 2 \cdot 1 } = 292825$

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