MAT 121 Test 1 Questions and Answers
A committee of six Congressmen will be selected from a group of six
Democrats and five Republicans. Find the number of ways of obtaining
exactly one Republican. - ----ANS:30
A committee of six Congressmen will be selected from a group of ten
Republicans and five Democrats. Find the number of ways of obtaining a
committee with exactly three Republicans. - ----ANS:1200
A contractor builds homes of 11 different models and presently has 3 lots to
build on. In how many different ways can he arrange homes on these lots?
Assume 3 different models will be built. - ----ANS:990
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? (Small is one,
Trout is another) - ----ANS:6936
A multiple-choice test consists of 8 questions with each question having 3
possible answers. How many different ways are there to mark the answers? -
----ANS:6561
A musician plans to perform 5 selections for a concert. If he can choose from
7 different selections, how many ways can he arrange his program? Round
the answer to the nearest whole number. - ----ANS:2520
A panel containing four on-off switches in a row is to be set. Assuming no
restrictions on individual switches, use the fundamental counting principle to
find the total number of possible panel settings. - ----ANS:16
A pool of possible jurors consists of 11 men and 13 women. How many
different juries consisting of 5 men and 7 women are possible? -
----ANS:792792
A sports shop sells tennis rackets in 4 different weights, 3 types of string, and
3 grip sizes. How many different rackets could they sell? - ----ANS:36
, A student is told to work any 7 out of 10 questions on an exam. In how many
different ways can he complete the exam? (The correctness of his answers
has no bearing.) Round the answer to the nearest whole number. -
----ANS:120
After rolling the first ball of a frame in a game of 10-pin bowling, how many
different pin configurations can remain (assuming all configurations are
physically possible)? - ----ANS:1024
Among the 2,598,960 possible 5-card poker hands from a standard 52-card
deck, how many contain at least one face card? - ----ANS:complement of no
face cards
1940952
Among the 2,598,960 possible 5-card poker hands from a standard 52-card
deck, how many contain at least one queen? - ----ANS:complement of no
queens
886656
Amy, Brenda, Chuck, Deirdre, and Early have reserved five seats in a row at
the theater, starting at an aisle seat. In how many ways can they arrange
themselves? - ----ANS:120
An electronics store receives a shipment of 40 graphing calculators, including
4 that are defective. Four of the calculators are selected to be sent to a local
high school. How many of these selections will contain no defective
calculators? - ----ANS:58905
At a lumber company, shelves are sold in 4 types of wood, 5 different widths
and 5 different lengths. How many different types of shelves could be
ordered? - ----ANS:100
At a wedding reception, the bride and groom and three attendants will form a
receiving line. How many ways can they be arranged in each of following
cases?
A) Any order will do. - ----ANS:120
At a wedding reception, the bride and groom and three attendants will form a
receiving line. How many ways can they be arranged in each of following
cases?
A committee of six Congressmen will be selected from a group of six
Democrats and five Republicans. Find the number of ways of obtaining
exactly one Republican. - ----ANS:30
A committee of six Congressmen will be selected from a group of ten
Republicans and five Democrats. Find the number of ways of obtaining a
committee with exactly three Republicans. - ----ANS:1200
A contractor builds homes of 11 different models and presently has 3 lots to
build on. In how many different ways can he arrange homes on these lots?
Assume 3 different models will be built. - ----ANS:990
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? (Small is one,
Trout is another) - ----ANS:6936
A multiple-choice test consists of 8 questions with each question having 3
possible answers. How many different ways are there to mark the answers? -
----ANS:6561
A musician plans to perform 5 selections for a concert. If he can choose from
7 different selections, how many ways can he arrange his program? Round
the answer to the nearest whole number. - ----ANS:2520
A panel containing four on-off switches in a row is to be set. Assuming no
restrictions on individual switches, use the fundamental counting principle to
find the total number of possible panel settings. - ----ANS:16
A pool of possible jurors consists of 11 men and 13 women. How many
different juries consisting of 5 men and 7 women are possible? -
----ANS:792792
A sports shop sells tennis rackets in 4 different weights, 3 types of string, and
3 grip sizes. How many different rackets could they sell? - ----ANS:36
, A student is told to work any 7 out of 10 questions on an exam. In how many
different ways can he complete the exam? (The correctness of his answers
has no bearing.) Round the answer to the nearest whole number. -
----ANS:120
After rolling the first ball of a frame in a game of 10-pin bowling, how many
different pin configurations can remain (assuming all configurations are
physically possible)? - ----ANS:1024
Among the 2,598,960 possible 5-card poker hands from a standard 52-card
deck, how many contain at least one face card? - ----ANS:complement of no
face cards
1940952
Among the 2,598,960 possible 5-card poker hands from a standard 52-card
deck, how many contain at least one queen? - ----ANS:complement of no
queens
886656
Amy, Brenda, Chuck, Deirdre, and Early have reserved five seats in a row at
the theater, starting at an aisle seat. In how many ways can they arrange
themselves? - ----ANS:120
An electronics store receives a shipment of 40 graphing calculators, including
4 that are defective. Four of the calculators are selected to be sent to a local
high school. How many of these selections will contain no defective
calculators? - ----ANS:58905
At a lumber company, shelves are sold in 4 types of wood, 5 different widths
and 5 different lengths. How many different types of shelves could be
ordered? - ----ANS:100
At a wedding reception, the bride and groom and three attendants will form a
receiving line. How many ways can they be arranged in each of following
cases?
A) Any order will do. - ----ANS:120
At a wedding reception, the bride and groom and three attendants will form a
receiving line. How many ways can they be arranged in each of following
cases?
