Sampling Distribution of Proportion Worksheet

**Page 1**

1.

A fashion apparel store gives choice to its clients to order T-shirts as per their personal tastes & preferences in terms of

Size: small, medium, large, extra large

Color: white, ivory, pastel brown, pastel yellow, gray

Texture: pure wool, synthetics, silk, cotton,

Style: plain (for men) & embroidered (for ladies), printed (for children)

How many types of orders can be placed if a client chooses one texture, one size, one color and one style?

Size: small, medium, large, extra large

Color: white, ivory, pastel brown, pastel yellow, gray

Texture: pure wool, synthetics, silk, cotton,

Style: plain (for men) & embroidered (for ladies), printed (for children)

How many types of orders can be placed if a client chooses one texture, one size, one color and one style?

a. | 192 | ||

b. | 16 | ||

c. | 420 | ||

d. | 240 |

Types of orders possible for a client = Number of possible combinations

Types of orders possible for a client if he chooses one texture, one size, one colour and one style = 4 × 5 × 4 × 3 = 240.

Correct answer : (4)

2.

How many 5-digit numbers (not starting with 0) can be made out of digits 0 - 9, if the numbers can be used only once?

a. | 252 | ||

b. | 30240 | ||

c. | 27216 | ||

d. | 100000 |

The first digit cannot be a zero, so the first place can be filled by any of the 9 numbers from 1 to 9.

Since the numbers are used only once, the second place can be filled in 9 ways.

[0 to 9 excluding the digit used in first place.]

The third place can be filled in 8 ways.

The fourth place can be filled in 7 ways.

The fifth place can be filled in 6 ways.

The total number of 5 digit numbers possible = 9 × 9 × 8 × 7 × 6 = 27216

Correct answer : (3)

3.

A television news director wishes to use three news stories on an evening show. One story will be the lead story, one will be the second story, and the last will be a closing story. If the director has a total of ten stories to choose from, how many possilbe ways can the program be set up?

a. | 6 | ||

b. | 120 | ||

c. | 3 | ||

d. | 720 |

We have to choose 3 stories from the given 10 stories, since the order is important, this can be done in

[Simplify.]

Hence, the program can be set up in 720 possible ways.

Correct answer : (4)

4.

How many combinations of 6 objects are there, taken 4 at a time?

a. | 15 | ||

b. | 24 | ||

c. | 360 | ||

d. | 4 |

In this case order is not important, so we go for combinations.

The number of combinations of 4 objects selected from 6 objects is denoted by

[Substitute

Hence, 15 combinations of 6 objects are there, taken 4 at a time.

Correct answer : (1)

5.

A committee of 4 men and 3 women is to be chosen from 6 men and 6 women. How many different possibilities are there?

a. | 300 | ||

b. | 43200 | ||

c. | 792 | ||

d. | 3 |

Here, one must select 3 women from 6 women, which can be done in

4 men can be selected from 6 men in

Using the fundamental counting rule, the total number of different ways =

[Simplify.]

So, there are 300 possible ways to select a committee of 4 men and 3 women.

Correct answer : (1)

6.

In a shelf there are 10 different math books, 8 different physics books, and 4 different psychology books. A student must select one book of each type. How many different ways can this be done?

a. | 32 | ||

b. | 320 | ||

c. | 22 | ||

d. | 80 |

Number of ways a physics book can be selected = 8

Number of ways a psychology book can be selected = 4

Selecting one book of each type = number of ways of selecting a math book × number of ways of selecting a physics book × number of ways of selecting a psychology book

Selecting one book of each type = 10 × 8 × 4 = 320

[Substitute.]

So, the number of ways in which a student can select one book of each type is 320.

Correct answer : (2)

7.

How many different 3-color code stripes can be made on a cloth if each code consists of the colors red, blue, green, violet and yellow? All colors are used only once.

a. | 243 | ||

b. | 60 | ||

c. | 125 | ||

d. | 15 |

The first color on the stripe can be choosen in 5 ways.

Number of ways the second color on the stripe can be choosen = 4

[Since colors cannot be repeated, we are left with 4 colors to choose.]

Number of ways the third color on the stripe can be choosen = 3

[Since colors cannot be repeated, we are left with 3 colors to choose.]

Total number of different 3-color code = number of ways of selecting the first stripe × number of ways of selecting the second stripe ×number of ways of selecting the third stripe

Total number of different 3-color code = 5 × 4 × 3 = 60

So, the total number of different 3-color code stripes is 60.

Correct answer : (2)

8.

There are three cities A, B, C. There are 5 major roads from city A to city B and 4 major roads from city B to city C. How many different routes can be covered while travelling from city A to city C passing through city B?

a. | 20 | ||

b. | 9 | ||

c. | 4 | ||

d. | 5 |

Number of ways a road can be selected between city B and city C = 4

Number of different routes that can be covered while travelling from city A to city C passing through city B = Number of ways a road can be selected between city A and city B × Number of ways a road can be selected between city B and city C = 5 × 4 = 20

So, the total number of different routes that can be covered while travelling from city A to city C passing through city B is 20.

Correct answer : (1)

9.

In how many ways can a boy select 3 red balls and 4 green balls from a box containing 6 balls of each kind?

a. | 300 | ||

b. | _{12}C_{7} | ||

c. | 3 | ||

d. | 12 |

[Selecting 3 balls from 6.]

Number of ways a green ball can be selected =

[Selecting 4 balls from 6.]

Number of ways of selecting 3 red balls and 4 green balls = Number of ways of selecting 3 red balls × Number of ways of selecting 4 green balls =

Number of ways of selecting 3 red balls and 4 green balls = 20 × 15 = 300

[

So, the number of many ways in which a boy can select 3 red balls and 4 green balls is 300.

Correct answer : (1)

10.

A football team manager has to select a team. He has 3 goalkeepers, 6 defenders, 7 midfielders, 6 attackers to choose from. He decides to go for 4 defenders, 3 midfielders, 3 attackers. How many ways can he choose his team?

a. | _{22}C_{11} | ||

b. | 36 | ||

c. | 8 | ||

d. | 31500 |

Number of ways 4 defenders can be selected from 6 defenders =

Number of ways 3 midfielders can be selected from 7 midfielders =

Number of ways 3 attackers can be selected from 6 attackers =

Total number of ways the team can be choosen = number of ways of selecting a goalkeeper × number of ways of selecting a defender × number of ways of selecting a midfielder × number of ways of selecting an attacker

Total number of ways the team can be choosen =

[Substitute.]

Total number of ways the team can be choosen = 3 × 15 × 35 × 20 = 31500

[Simplify.]

So, a football team manager can select a team in 31500 ways.

Correct answer : (4)