Chapter Test Combinations
Chapter
Chapter 3
Section
Chapter Test Combinations
Solutions 19 Videos

How many ways are there to select four people from a group of nine people, without regard to order?

A 36

B 262144

C 126

D 3024

Q1

What is the total number of subsets of a set of 10 elements?

A 1024

B 1023

C 100

D 20

Q2

Using Pascal’s method, what is _7C_3 + _70_4?

A. \displaystyle _8C_3

B. \displaystyle _8C_4 

C. \displaystyle _8C_5 

D. \displaystyle _7C_5 

Q3

What is the number of arrangements of three red and two green blocks?

A. \displaystyle \frac{5!}{3!2!}

B. \displaystyle 3!2! 

C. \displaystyle 5! 

D. \displaystyle \frac{6!}{3!2!} 

Q4

In how many ways could a 6-member committee be formed from a 16-member club, if the president and secretary must be on the committee?

Q5

You found seven library books that you would like to take out, but the maximum is four. In how many ways could you select the four books?

Q6

How many quadrilaterals can be formed from the vertices of an octagon?

Q7

How many permutations are there of the letters in the word RELATIONS, if the vowels must be in alphabetical order?

Q8

a) How are _8C_3 and _8P_3 related?

b) Explain this relationship. Include an example to support your explanation.

Q9

Two balls are selected from a bag with five white and nine black balls. What is the probability that both balls are black?

Q10

What is the coefficient of p^4q^6 in the expansion of (p + q)^{10}?

Q11

Use two methods to show the number of ways 18 members of a rugby team could be assigned to 81X triple hotel rooms.

Q12

a) Describe the relationship between Pascal’s triangle and combinations.

b) Write Pascal’s method as it relates to both the entries in Pascal’s triangle and t0 combinations.

Q13

Alternately subtract and add successive terms in a row of Pascal’s triangle. For example, in row 4, 1- 4 + 6 - 4 +1.

a) Investigate a few rows and describe the results.

b) Relate the results to combinations and provide a formula in terms of _nC_r.

Q14

Mario orders a pizza with 3 toppings, chosen from 15 available toppings.

a) In how many ways could mushrooms or olives be included in his toppings?

b) Would the result in part a) be greater or less if he orders 4 toppings? Explain.

Q15

A package of 50 computer chips contains 45 that are perfect and 5 that are defective. If 2 chips are selected at random, what is the probability that

a) neither is defective?

b) both are defective?

c) only one is defective?

Q16

The tens. jacks. queens, kings, and aces are removed from a standard deck of cards. From these cards, four are chosen. What is the probability that

a) all are queens?

b) all are red?

c) two are face cards?

d) there is at least one ace?

e) there are at least one ace and one king?