Permutations, Combinations, and Counting Principles Quiz

1) In how many ways can 4 books be arranged on a shelf?

16

24

12

8

4!=24.

Explanation

4!=24.

2) The number of ways to choose 0 objects from n objects is 1.

True

False

Empty selection counted once.

Explanation

Empty selection counted once.

3) How many distinct 5-digit numbers using digits 1–5 without repetition?

60

120

100

1200

5!=120.

Explanation

5!=120.

4) Committee: choose 2 men from 6 and 2 women from 5.

45

90

150

180

15×10=150.

Explanation

15×10=150.

5) How many ways can a president and vice-president be chosen from 8 students?

28

56

64

72

8×7=56.

Explanation

8×7=56.

6) How many 3-letter words from A,B,C,D if repetition allowed?

12

24

64

16

4^3=64.

Explanation

4^3=64.

7) Which are true for permutations?

Order matters

No repetitions allowed

Order does not matter

Used for arrangements

Permutations are ordered arrangements.

Explanation

Permutations are ordered arrangements.

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8) Distribute 5 identical balls into 3 distinct boxes.

21

10

15

5

C(7,2)=21.

Explanation

C(7,2)=21.

9) How many diagonals in convex 8-gon?

16

20

24

28

n(n−3)/2=20.

Explanation

n(n−3)/2=20.

10) P(n,r)=n!/(n−r)!

True

False

Standard permutation formula.

Explanation

Standard permutation formula.

11) How many ways can you arrange the letters in the word 'LEVEL'?

60

120

30

20

5!/(2!2!)=30.

Explanation

5!/(2!2!)=30.

12) Which are examples of combinations?

Choosing 3 students from 10

Arranging 3 books

Selecting 5 cards from a deck

Assigning student positions

Combinations ignore order.

Explanation

Combinations ignore order.

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13) C(n,r)=C(n,n−r).

True

False

Choosing r equals excluding n−r.

Explanation

Choosing r equals excluding n−r.

14) How many 4-digit numbers using digits 1–6 without repetition?

360

120

720

256

6P4=360.

Explanation

6P4=360.

15) Match: 1.n! 2.C(n,r) 3.n^r

choose r without order

arrange n objects

select r with repetition

Definitions of factorial, combinations, repeated selections.

Explanation

Definitions of factorial, combinations, repeated selections.

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Permutations, Combinations, and Counting Principles Quiz

1) In how many ways can 4 books be arranged on a shelf?

2)

What first name or nickname would you like us to use?

2) The number of ways to choose 0 objects from n objects is 1.

3) How many distinct 5-digit numbers using digits 1–5 without repetition?

4) Committee: choose 2 men from 6 and 2 women from 5.

5) How many ways can a president and vice-president be chosen from 8 students?

6) How many 3-letter words from A,B,C,D if repetition allowed?

7) Which are true for permutations?

8) Distribute 5 identical balls into 3 distinct boxes.

9) How many diagonals in convex 8-gon?

10) P(n,r)=n!/(n−r)!

11) How many ways can you arrange the letters in the word 'LEVEL'?

12) Which are examples of combinations?

13) C(n,r)=C(n,n−r).

14) How many 4-digit numbers using digits 1–6 without repetition?

15) Match: 1.n! 2.C(n,r) 3.n^r