Exercises: Permutations

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

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

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Recall / Warm-Up

These problems review prerequisite skills.

A student has 4 shirts and 3 pairs of pants. Using the fundamental counting principle, how many different outfits can the student make?

What is the value of the expression $n!$ when $n = 0$ ?

Which scenario requires counting ordered arrangements rather than unordered groups?

Choosing 3 toppings for a pizza from a menu of 10

Selecting a president, vice president, and treasurer from 10 club members

Picking 5 students to form a study group from a class of 30

Drawing 3 raffle tickets from a bowl of 50

Use the permutation formula or factorial simplification to compute each value.

Evaluate $\frac{7!}{5!}$ .

What is $P(6, 2)$ ?

720

Compute $P(9, 3)$ .

Compute $P(5, 5)$ .

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