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Question : Evaluate the combination 1) C(13, 6) A) 10,080 B) 1716 C) 617,760 : 2151692

**MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.**

**Evaluate the combination.**

1) C(13, 6)

A) 10,080

B) 1716

C) 617,760

D) 8,648,640

2) C(10, 0)

A) 1

B) 3,628,800

C) 1,814,400

D) 907,200

3) C(16, 1)

A) 16

B) 16!

C) 16! - 10

D) 2

4) C(29, 29)

A) 1

B) 2

C) 29!

D) 29! - 5

5) C(s, 8)

A) s!

B) s!/(s – 8)!

C) s!/s!(s – 8)!

D) s!/8!

6) C(s, p)

A) s!/p!(s – p)!

B) 1/p!(s – p)!

C) s!/p!

D) s!/(s – p)!

**Of the 2,598,960 different five-card hands possible from a deck of 52 playing cards, how many would contain the following cards?**

7) All four tens

A) 48 hands

B) 144 hands

C) 192 hands

D) 1152 hands

8) All black cards

A) 263,120 hands

B) 32,890 hands

C) 131,560 hands

D) 65,780 hands

9) No face cards

A) 658,008 hands

B) 639,730 hands

C) 319,865 hands

D) 127,946 hands

10) All spades

A) 2574 hands

B) 3861 hands

C) 143 hands

D) 1287 hands

11) Two black cards and three red cards

A) 845,000 hands

B) 422,500 hands

C) 1,267,500 hands

D) 1,690,000 hands

**Solve the problem.**

12) How many ways can a committee of 4 be selected from a club with 12 members?

A) 248 ways

B) 11,880 ways

C) 495 ways

D) 24 ways

13) In how many ways can a student select 8 out of 10 questions to work on an exam?

A) 90 ways

B) 16 ways

C) 45 ways

D) 100,000,000 ways

14) How many ways can a committee of 5 be selected from a club with 10 members?

A) 252 ways

B) 50 ways

C) 100,000 ways

D) 30,240 ways

15) If the police have 7 suspects, how many different ways can they select 5 for a lineup?

A) 2520 ways

B) 21 ways

C) 42 ways

D) 35 ways

16) In how many ways can a group of 9 students be selected from 10 students?

A) 1 way

B) 9 ways

C) 10 ways

D) 90 ways

17) A group of five entertainers will be selected from a group of twenty entertainers that includes Small and Trout. In how many ways could the group of five include at least one of the entertainers Small and Trout?

A) 6936 ways

B) 11,628 ways

C) 15,504 ways

D) 8568 ways

18) A class has 10 boys and 12 girls. In how many ways can a committee of four be selected if the committee can have at most two girls?

A) 4410 ways

B) 5665 ways

C) 5170 ways

D) 4620 ways

19) The chorus has six sopranos and eight baritones. In how many ways can the director choose a quartet that contains at least one soprano?

A) 1071 ways

B) 931 ways

C) 986 ways

D) 1001 ways

20) Three noncollinear points determine a triangle. How many triangles can be formed with 8 points, no three of which are collinear?

A) 6720 triangles

B) 24 triangles

C) 336 triangles

D) 56 triangles

**Decide whether the situation involves permutations or combinations.**

21) A batting order for 9 players for a baseball game.

A) Permutation

B) Combination

22) An arrangement of 4 people for a picture.

A) Permutation

B) Combination

23) A committee of 7 delegates chosen from a class of 27 students to bring a petition to the administration.

A) Permutation

B) Combination

24) A selection of a chairman and a secretary from a committee of 7 people.

A) Permutation

B) Combination

25) A sample of 8 items taken from 66 items on an assembly line.

A) Permutation

B) Combination

26) A blend of 4 spices taken from 7 spices on a spice rack.

A) Permutation

B) Combination

**Solve the problem.**

27) If you toss five fair coins, in how many ways can you obtain at least one head?

A) 32 ways

B) 15 ways

C) 16 ways

D) 31 ways

28) If you toss six fair coins, in how many ways can you obtain at least two heads?

A) 64 ways

B) 58 ways

C) 63 ways

D) 57 ways

29) If you toss four fair coins, in how many ways can you obtain at least one head?

A) 4 ways

B) 16 ways

C) 5 ways

D) 15 ways

30) How many 5-card poker hands consisting of 3 aces and 2 kings are possible with an ordinary 52-card deck?

A) 6 five-card hands

B) 288 five-card hands

C) 12 five-card hands.

D) 24 five-card hands

31) A bag contains 7 apples and 5 oranges. If you select 6 pieces of fruit without looking, how many ways can you get 6 apples?

A) 7 ways

B) 35 ways

C) 14 ways

D) 12 ways

32) A bag contains 5 apples and 3 oranges. If you select 4 pieces of fruit without looking, how many ways can you get 4 oranges?

A) 15 ways

B) 5 ways

C) 0 ways

D) 8 ways

33) A bag contains 5 apples and 3 oranges. If you select 4 pieces of fruit without looking, how many ways can you get exactly 3 apples?

A) 60 ways

B) 180 ways

C) 30 ways

D) 20 ways

34) If a license plate consists of four digits, how many different licenses could be created having at least one digit repeated.

A) 4960 licenses

B) 10,000 licenses

C) 3024 licenses

D) 5040 licenses

35) If a license plate consists of two letters followed by four digits, how many different licenses could be created having at least one letter or digit repeated.

A) 3,484,000 licenses

B) 3,276,000 licenses

C) 6,760,000 licenses

D) 4,009,824 licenses

36) How many different three-digit numbers can be written using digits from the set {1, 2, 3, 4, 5} without any repeating digits?

A) 120 three-digit numbers

B) 10 three-digit numbers

C) 60 three-digit numbers

D) 20 three-digit numbers

37) How many different three-number "combinations" are possible on a combination lock having 20 numbers on its dial? Assume that no numbers repeat. (Combination locks are really permutation locks.)

A) 6.9768 × 10^{5} three-number "combinations"

B) 1.1628 × 10^{5} three-number "combinations"

C) 6840 three-number "combinations"

D) 2.3256 × 10^{5} three-number "combinations"

38) How many two-digit counting numbers do not contain any of the digits 1, 3, or 9?

A) 49 numbers

B) 81 numbers

C) 72 numbers

D) 42 numbers

39) How many three-digit counting numbers do not contain any of the digits 1, 5, 7, 8, or 9?

A) 125 numbers

B) 48 numbers

C) 100 numbers

D) 64 numbers