Daily math problems for May 9, 2026 — Combinatorics, Compound Interest, Algebra

$\left(\genfrac{}{}{0px}{}{10}{3}\right)={\displaystyle \frac{10!}{3!\cdot 7!}}={\displaystyle \frac{10\cdot 9\cdot 8}{3!}}={\displaystyle \frac{720}{6}}=120$.

The convention: 'committee' implies order doesn't matter — a committee of {Alice, Bob, Carol} is the same as {Carol, Alice, Bob}. That's exactly when you use $\left(\genfrac{}{}{0px}{}{n}{k}\right)$ instead of $P(n,k)$.

This is a future-value-of-annuity problem: $$FV=P\cdot \frac{(1+i{)}^n-1}{i}$$ where $P=200$, $i=0.06\mathrm{/}12=0.005$, $n=30\cdot 12=360$.

$(1.005{)}^{360}\approx 6.023$. So $FV\approx 200\cdot {\displaystyle \frac{6.023-1}{0.005}}=200\cdot 1004.5\approx \mathrm{\$}\mathrm{200,900}$.

Note: you contributed only $200\cdot 360=\mathrm{\$}\mathrm{72,000}$. The other $\approx \mathrm{\$}\mathrm{129,000}$ is compounding.

Inside out. First: $g(2)=2\cdot 2-3=1$. Then: $f(1)=1^2+1=2$.