Probability Pt. 2

From a group of 16 smokers and 22 nonsmokers, a researcher wants to randomly select 4 smokers and 4 nonsmokers for a study.

In how many ways can the study group be selected?

13313300

A legislative committee consists of 5 Democrats and 4 Republicans. A delegation of 3 is to be selected to visit a small Pacific island republic.

In how many ways committee be selected?

84

Andy has 20 toys, including a talking cowboy doll, in his toy box.

In how many ways can Andy select a group of 5 toys if the cowboy doll has to be one of the five?

3876

Andy has 20 toys, including a talking cowboy doll, in his toy box.

In how many ways can Andy arrange 5 of his 20 toys on a shelf if the cowboy doll has to be in the center?

93,024

Isabella has different books to arrange on a shelf: 4 blue, 3 green, and 2 red.

In how many ways can the books be arranged if books of the same color are identical?

1260

In how many ways can a sample of 5 avocados be chosen from a crate of 30 avocados?

142,506

Makayla's financial advisor has given her a list of 9 potential investments and has asked her to select and rank her favorite five.

In how many different ways can she do this?

15,120

A legislative committee consists of 5 Democrats and 4 Republicans. A delegation of 3 is to be selected to visit a small Pacific island republic.

How many delegations would include at least 1 Republican?

74

The U.S. Postal Service currently uses 5-digit ZIP Codes in most areas. How many ZIP Codes are possible if the first number cannot be 0?

90,000

If an ice-cream shop offers 2 types of cones, 4 flavors of ice cream, and 6 toppings, then how many ways are there to select a single cone with one flavor of ice cream?

48

A chapter of union Local 715 has 35 members. In how many different ways can the chapter select a president, a vice president, a treasurer, and a secretary.

1256640

How many ways can the letters of the word “LITTLE” be arranged

180

A small department of 5 people decide to form a hiring comitee. THe only restriciton on size is it must be at least 2 members how many committees are possible

26