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Counting and Combinatorics
Counting and Combinatorics
3 questions
Difficulty 2-4
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Foundation
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2 foundation
1 intermediate
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foundation (2/10)
compute
(
k
n
)
counts the number of ways to choose
k
items from
n
distinct items. Which identity is correct?
Hide and think first
A.
(
k
n
)
=
n
k
/
k
!
: matches the permutation formula
B.
(
k
n
)
=
(
n
−
k
n
)
: choosing
k
items is equivalent to leaving out
n
−
k
C.
(
k
n
)
=
n
(
k
−
1
n
−
1
)
: always strictly more than
n
D.
(
k
n
)
=
(
k
n
−
1
)
⋅
(
k
−
1
n
−
1
)
: product of adjacent values
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