Exercise · ZW-BINOMIAL-COEFFICIENT-004 · ★☆☆ Basic
Compute \(\dbinom{10}{0}+\dbinom{10}{10}\).
Choose one option.
Show answer
- C. 2
Explanation
There is exactly one empty subset and exactly one subset with all 10 elements: \(1+1=2\).
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
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- ZW-BINOMIAL-COEFFICIENT-003 Compute dbinom97.
- ZW-BINOMIAL-COEFFICIENT-005 Compute dbinom73+dbinom74.
- 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…