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Olympiad
Easy
Combinatorics
10–12
What is
(
10
3
)
+
(
10
4
)
\binom{10}{3} + \binom{10}{4}
(
3
10
)
+
(
4
10
)
?
Quanto vale
(
10
3
)
+
(
10
4
)
\binom{10}{3} + \binom{10}{4}
(
3
10
)
+
(
4
10
)
?
Answer options
A.
330
B.
462
C.
120
D.
210
Check Answer
Solution
Step 1 of 3
1.
Pascal's rule says
(
n
k
)
+
(
n
k
+
1
)
=
(
n
+
1
k
+
1
)
\binom{n}{k} + \binom{n}{k+1} = \binom{n+1}{k+1}
(
k
n
)
+
(
k
+
1
n
)
=
(
k
+
1
n
+
1
)
.
Next step
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