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Python 3, 126 111 108108 103 bytes

def f(c,a):x=sorted([a.count(i)for i in set(a)]);return int(([300,777,200,100,10][len(x)*(x[-1]!=3)]+c)//100)

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Python 3, 126 111 108 bytes

def f(c,a):x=sorted([a.count(i)for i in set(a)]);return int(([300,777,200,100,10][len(x)*(x[-1]!=3)]+c)/100)

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Python 3, 126 111 108 103 bytes

def f(c,a):x=sorted([a.count(i)for i in set(a)]);return([300,777,200,100,10][len(x)*(x[-1]!=3)]+c)//100

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Python 3, 126 111111 108 bytes

def f(c,a):
	x=sortedx=sorted([a.count(i)for i in set(a)])
	return;return int(([300,777,200,100,10][len(x)*(x[-1]!=3)]+c)/100)

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Python 3, 126 111 bytes

def f(c,a):
	x=sorted([a.count(i)for i in set(a)])
	return int(([300,777,200,100,10][len(x)*(x[-1]!=3)]+c)/100)

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Python 3, 126 111 108 bytes

def f(c,a):x=sorted([a.count(i)for i in set(a)]);return int(([300,777,200,100,10][len(x)*(x[-1]!=3)]+c)/100)

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Python 3, 126126 111 bytes

lambdadef f(c,a:int(({'1111':10,'112':100,'22':200,'13':300,'4'):777}.get(''.join(sorted([str
	x=sorted(a[a.count(i))for i in set(a)])
	return int(([300,777,200,100,10][len(x)*(x[-1]!=3)+c]+c)/100)

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Python 3, 126 bytes

lambda c,a:int(({'1111':10,'112':100,'22':200,'13':300,'4':777}.get(''.join(sorted([str(a.count(i))for i in set(a)])))+c)/100)

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Python 3, 126 111 bytes

def f(c,a):
	x=sorted([a.count(i)for i in set(a)])
	return int(([300,777,200,100,10][len(x)*(x[-1]!=3)]+c)/100)

Try it online!

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