С^(y+1)_(x)=x!/((y+!)!*(x-y-1)!);
С^(y)_(x)=x!/((y)!*(x-y)!);
С^(y+2)_(x):С^(y+1)_(x):С^(y)_(x)=42:35:20 ⇒
С^(y+2)_(x):С^(y+1)_(x)=42:35⇒(x-y-1)/(y+2)=42/35
С^(y+1)_(x):С^(y)_(x)=45:20⇒ (x-y)/(y+1)=35/20
Система:
{(x-y-1)/(y+2)=42/35⇒ 5x-5y-5=6y+12 ⇒ 5x=11y+17
{(x-y)/(y+1)=35/20 ⇒ 4x-4y=7y+7 ⇒ 4x=11y+7
(11y+187/5=(11y+7)/4
y=3
x=10