Exercises: Combinations

Work through each section in order. Show your work where indicated.

Grade 10·18 problems·~25 min·ACT Math·topic·act-sp-counting-comb

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Recall / Warm-Up

These problems review prerequisite skills.

What is the value of the expression below?
$\frac{6!}{4!}$

720

Which statement correctly explains why $C(5, 3)$ is less than $P(5, 3)$ ?

Combinations use smaller numbers in the formula

Combinations ignore the order of the selected items, so each group is counted once instead of multiple times

Combinations only apply when fewer than half the items are selected

Permutations add items while combinations subtract them

A club with 8 members is choosing a president and a vice president. Does order matter in this selection?

Yes — assigning Ana as president and Ben as VP is different from assigning Ben as president and Ana as VP

No — the same two people are chosen either way

Only if the club has more than 10 members

Only if the president and VP have different responsibilities

Use the combination formula to compute each value.

Compute $C(6, 2)$ .

What is $C(8, 3)$ ?

336

112

Compute $C(10, 4)$ .

What is $C(7, 5)$ ?

2520

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