Exercise · ZW-BINOMIAL-COEFFICIENT-001 · ★☆☆ Basic
Compute \(\dbinom{6}{2}\).
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- B. 15
Explanation
\(\dbinom{6}{2}=\dfrac{6!}{2!\,4!}=\dfrac{6\cdot 5}{2}=15\). The value \(30\) forgets to divide by \(2!\).
Review the concept: Binomial coefficient
The binomial coefficient \(\binom{n}{k}\), for integers \(0\le k\le n\), is the number of \(k\)-element subsets of a set with \(n\) elements.
\[\binom{n}{k}=\frac{n!}{k!\,(n-k)!}\]
More practice problems: binomial coefficient
- ZW-BINOMIAL-COEFFICIENT-002 How many 3-element subsets does \1,2,3,4,5\ have?
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- ZW-BINOMIAL-COEFFICIENT-006 Compute dbinom2018.
- ZW-BINOMIAL-COEFFICIENT-007 Which expression equals dbinomnk for 0≤ k≤ n?
- ZW-BINOMIAL-COEFFICIENT-008 Compute ∑_k=0^5dbinom5k.
- ZW-BINOMIAL-COEFFICIENT-009 A grid is traversed from the bottom-left corner to the top-right corner using 4 steps right and 3 s…