Exercises: Combinations

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

Grade 10·21 problems·~29 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

What is $P(4, 2)$ ?

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

No — the same two people are chosen either way

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

Only if the club has more than 10 members

Only if some members are more experienced than others

A shop has 3 shirts and 2 pairs of pants. An outfit is one shirt and one pair of pants. How many different outfits are possible?

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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