Daily Math · 2026-05-09

Question 1

From a group of 10 people, how many ways can a committee of 3 be chosen?

Accepted Answer

$\binom{10}{3} = \dfrac{10!}{3! \cdot 7!} = \dfrac{10 \cdot 9 \cdot 8}{3!} = \dfrac{720}{6} = 120$.

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 $\binom{n}{k}$ instead of $P(n,k)$.

Answer

$30$

Answer

$120$

Answer

$720$

Answer

$1000$

Question 2

You invest \$200 at the end of each month into an account paying 6% APR, compounded monthly. After 30 years, approximately how much is in the account?

Accepted Answer

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

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

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

Answer

\$72,000

Answer

\$120,000

Answer

\$200,000

Answer

\$1,000,000

Question 3

If $f(x) = x^2 + 1$ and $g(x) = 2x - 3$, what is $f(g(2))$?

Accepted Answer

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

Answer

$1$

Answer

$2$

Answer

$5$

Answer

$11$

Problems & worked solutions

Problem 1 — Combinatorics

Problem 2 — Compound Interest

Problem 3 — Algebra