Permutations, Combinations, and Counting Principles Quiz

1) 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.

2) 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.

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

16

24

12

8

4!=24.

Explanation

4!=24.

4) 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.

Submit

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

True

False

Empty selection counted once.

Explanation

Empty selection counted once.

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

60

120

100

1200

5!=120.

Explanation

5!=120.

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

12

24

64

16

4^3=64.

Explanation

4^3=64.

8) 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.

Submit

9) C(n,r)=C(n,n−r).

True

False

Choosing r equals excluding n−r.

Explanation

Choosing r equals excluding n−r.

10) Distribute 5 identical balls into 3 distinct boxes.

21

10

15

5

C(7,2)=21.

Explanation

C(7,2)=21.

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

360

120

720

256

6P4=360.

Explanation

6P4=360.

12) 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.

Submit

13) How many diagonals in convex 8-gon?

16

20

24

28

n(n−3)/2=20.

Explanation

n(n−3)/2=20.

14) P(n,r)=n!/(n−r)!

True

False

Standard permutation formula.

Explanation

Standard permutation formula.

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

45

90

150

180

15×10=150.

Explanation

15×10=150.

Permutations, Combinations, and Counting Principles Quiz

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

2)

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

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

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

4) Which are examples of combinations?

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

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

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

8) Which are true for permutations?

9) C(n,r)=C(n,n−r).

10) Distribute 5 identical balls into 3 distinct boxes.

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

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

13) How many diagonals in convex 8-gon?

14) P(n,r)=n!/(n−r)!

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