Question 1

In how many ways can you be dealt four cards from an ordinary deck of 52 cards? ​
A) 269,286
B) 270,725
C) 271,668
D) 270,735
E) 269,450

Accepted Answer

The number of ways to choose 4 cards from a deck of 52 is given by the combination formula C(52, 4) = 52! / (4!(52-4)!) = 270,725.

Question 2

A club consists of 16 men and 17 women. In how many ways can they choose a president, vice president, treasurer, and secretary, along with an advisory committee of six people? ​
A) 596,387,610,000
B) 1,022,862,306,928
C) 563,336,193,420
D) 498,094,571,520
E) 466,507,641,600

Accepted Answer

The answer of A club consists of 16 men and...

Question 3

Evaluate the expression.
​

Accepted Answer

The answer of Evaluate the expression.
​ ...

Question 4

How many different subsets can be chosen from a set of seven elements? ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of How many different subsets can be chosen...

Question 5

In how many ways can you be dealt three cards from an ordinary deck of 52 cards?

Accepted Answer

The answer of In how many ways can you be...

Question 6

In how many ways can a full house of three jacks and two tens be obtained?

Accepted Answer

The answer of In how many ways can a full...

Question 7

An ice cream parlor has 34 different flavors. A super sundae allows a person to select 3 different flavors and 3 (out of 9) different toppings. How many different selections are possible?
​
Round amount to the nearest whole number.

Accepted Answer

The answer of An ice cream parlor has 34 different...

Question 8

Evaluate the expression.
​

Accepted Answer

The answer of Evaluate the expression.
​ ...

Question 9

In how many ways can a full house of three jacks and two tens be obtained? ​
A) 10
B) 24
C) 28
D) 32
E) 6

Accepted Answer

A full house in poker consists of three cards of one rank and two cards of another. For three jacks, there are $ \binom{4}{3} = 4 $ ways to choose which three of the four jacks to include. For two tens, there are $ \binom{4}{2} = 6 $ ways to choose which two of the four tens to include. Multiplying these together gives $ 4 \times 6 = 24 $ ways to get a full house of three jacks and two tens.

Question 10

Evaluate the expression. ​  ​
​
A) 95
B) 98
C) 94
D) 96
E) 100

Accepted Answer

The answer of Evaluate the expression. ​  ​
​
A) 95
B)...

Question 11

In how many ways can a diamond flush be obtained?

Accepted Answer

The answer of In how many ways can a diamond...

Question 12

Tom is leading a workshop for 23 people. He wants each person to meet every other person (shake hands once). How many handshakes occur?

Accepted Answer

The answer of Tom is leading a workshop for 23...

Question 13

Evaluate the expression. ​  ​
A) 216
B) 48
C) 576
D) 168
E) 288

Accepted Answer

The answer of Evaluate the expression. ​  ​
A) 216
B)...

Question 14

A club consists of 17 men and 18 women. In how many ways can they choose a president, vice president, treasurer, and secretary, along with an advisory committee of six people?
​
Round amount to the nearest whole number.

Accepted Answer

The answer of A club consists of 17 men and...

Question 15

An ice cream parlor has 33 different flavors. A super sundae allows a person to select 4 different flavors and 4 (out of 8) different toppings. How many different selections are possible? ​
A) 2,864,400
B) 971,890,920
C) 1,649,894,400
D) 68,745,600
E) 117,600

Accepted Answer

The number of ways to select 4 flavors out of 33 is given by the combination formula $C(n, k) = \frac{n!}{k!(n-k)!}$, where $n$ is the total number of items, and $k$ is the number of items to choose. So, for the flavors, it's $C(33, 4) = \frac{33!}{4!(33-4)!}$.For the toppings, since there are 8 to choose from and we want 4, it's $C(8, 4) = \frac{8!}{4!(8-4)!}$.The total number of different selections is the product of these two combinations: $C(33, 4) * C(8, 4)$.Calculating each:- $C(33, 4) = \frac{33!}{4!29!} = \frac{33 \times 32 \times 31 \times 30}{4 \times 3 \times 2 \times 1} = 40920$- $C(8, 4) = \frac{8!}{4!4!} = \frac{8 \times 7 \times 6 \times 5}{4 \times 3 \times 2 \times 1} = 70$Multiplying these together gives $40920 \times 70 = 2,864,400$.

Question 16

Evaluate the expression.
​

Accepted Answer

The answer of Evaluate the expression.
​ ...

Question 17

How many different subsets can be chosen from a set of eight elements?

Accepted Answer

The answer of How many different subsets can be chosen...

Question 18

Evaluate the expression. ​  ​
A) 154,431
B) 154,440
C) 154,433
D) 154,438
E) 154,437

Accepted Answer

The answer of Evaluate the expression. ​  ​
A) 154,431
B)...

Question 19

In how many ways can a club flush be obtained? ​
A) 154,440
B) 1,287
C) 2,598,764
D) 2,475,391
E) 1,382

Accepted Answer

A club flush in poker is a hand where all cards are clubs. There are 13 clubs in a deck, and a flush requires 5 cards, so the number of ways to get a club flush is the combination of 13 clubs taken 5 at a time, which is calculated as 13C5 = 1,287.

Question 20

Tom is leading a workshop for 15 people. He wants each person to meet every other person (shake hands once). How many handshakes occur? ​
A) 213
B) 105
C) 98
D) 210
E) 108

Accepted Answer

The total number of handshakes can be calculated using the formula for combinations: n(n-1)/2, where n is the number of people. For 15 people, it's 15(15-1)/2 = 105.

Quiz 12: The Nature of Counting

In how many ways can you be dealt four cards from an ordinary deck of 52 cards?

A club consists of 16 men and 17 women. In how many ways can they choose a president, vice president, treasurer, and secretary, along with an advisory committee of six people?

Evaluate the expression.

How many different subsets can be chosen from a set of seven elements?

In how many ways can you be dealt three cards from an ordinary deck of 52 cards?

In how many ways can a full house of three jacks and two tens be obtained?

An ice cream parlor has 34 different flavors. A super sundae allows a person to select 3 different flavors and 3 (out of 9) different toppings. How many different selections are possible? Round amount to the nearest whole number.

Evaluate the expression.

In how many ways can a full house of three jacks and two tens be obtained?

Evaluate the expression.

In how many ways can a diamond flush be obtained?

Tom is leading a workshop for 23 people. He wants each person to meet every other person (shake hands once). How many handshakes occur?

Evaluate the expression.

A club consists of 17 men and 18 women. In how many ways can they choose a president, vice president, treasurer, and secretary, along with an advisory committee of six people? Round amount to the nearest whole number.

An ice cream parlor has 33 different flavors. A super sundae allows a person to select 4 different flavors and 4 (out of 8) different toppings. How many different selections are possible?

Evaluate the expression.

How many different subsets can be chosen from a set of eight elements?

Evaluate the expression.

In how many ways can a club flush be obtained?

Tom is leading a workshop for 15 people. He wants each person to meet every other person (shake hands once) . How many handshakes occur?

Quiz 12: The Nature of Counting

In how many ways can you be dealt four cards from an ordinary deck of 52 cards? ​

A club consists of 16 men and 17 women. In how many ways can they choose a president, vice president, treasurer, and secretary, along with an advisory committee of six people? ​

Evaluate the expression. ​

How many different subsets can be chosen from a set of seven elements? ​

In how many ways can you be dealt three cards from an ordinary deck of 52 cards?

In how many ways can a full house of three jacks and two tens be obtained?

An ice cream parlor has 34 different flavors. A super sundae allows a person to select 3 different flavors and 3 (out of 9) different toppings. How many different selections are possible? ​ Round amount to the nearest whole number.

Evaluate the expression. ​

In how many ways can a full house of three jacks and two tens be obtained? ​

Evaluate the expression. ​ ​ ​

In how many ways can a diamond flush be obtained?

Tom is leading a workshop for 23 people. He wants each person to meet every other person (shake hands once). How many handshakes occur?

Evaluate the expression. ​ ​

A club consists of 17 men and 18 women. In how many ways can they choose a president, vice president, treasurer, and secretary, along with an advisory committee of six people? ​ Round amount to the nearest whole number.

An ice cream parlor has 33 different flavors. A super sundae allows a person to select 4 different flavors and 4 (out of 8) different toppings. How many different selections are possible? ​

Evaluate the expression. ​

How many different subsets can be chosen from a set of eight elements?

Evaluate the expression. ​ ​

In how many ways can a club flush be obtained? ​

Tom is leading a workshop for 15 people. He wants each person to meet every other person (shake hands once) . How many handshakes occur? ​

In how many ways can you be dealt four cards from an ordinary deck of 52 cards?

A club consists of 16 men and 17 women. In how many ways can they choose a president, vice president, treasurer, and secretary, along with an advisory committee of six people?

Evaluate the expression.

How many different subsets can be chosen from a set of seven elements?

An ice cream parlor has 34 different flavors. A super sundae allows a person to select 3 different flavors and 3 (out of 9) different toppings. How many different selections are possible? Round amount to the nearest whole number.

Evaluate the expression.

In how many ways can a full house of three jacks and two tens be obtained?

Evaluate the expression.

Evaluate the expression.

A club consists of 17 men and 18 women. In how many ways can they choose a president, vice president, treasurer, and secretary, along with an advisory committee of six people? Round amount to the nearest whole number.

An ice cream parlor has 33 different flavors. A super sundae allows a person to select 4 different flavors and 4 (out of 8) different toppings. How many different selections are possible?

Evaluate the expression.

Evaluate the expression.

In how many ways can a club flush be obtained?

Tom is leading a workshop for 15 people. He wants each person to meet every other person (shake hands once) . How many handshakes occur?