M5 Fundamental Counting Principle

Multiple Choice

DNA molecules include the base units adenine, thymine, cytosine, and guanine (A, T, C, and G). The sequence of base units along a strand of DNA encodes genetic information. In how many different sequences can A, T, C, and G be arranged along a short strand of DNA that has only 8 base units?

• 16,384

• 65,536

• 24

• 32

Multiple Choice

How many license plates of 3 symbols (letters and digits) can be made using at least 2 letters for each?

• 24,336

• 1,757,600

• 37,856

• 46,656

Multiple Choice

How many 3-letter code words can be formed if at least one of the letters is to be chosen from the vowels a, e, i, o, and u?

• 12,215

• 8,315

• 4,155

• 12,090

Multiple Choice

How many positive odd integers less than 10,000 can be written using the digits 3, 4, 6, 8, and 0?

• 125

• 625

• 60

• 3,125

Multiple Choice

You are going to set up a stereo system by purchasing separate components. In your price range you find 5 different speakers, 8 different compact disc players, and 23 different speaker systems. If you want one of each of these components, how many different stereo systems are possible?

• 36

• 900

• 770

• 920

Multiple Choice

To keep computer files secure, many programs require the user to enter a password. The shortest allowable passwords are typically six characters long and can contain both numbers and letters. How many six-character passwords are possible if characters cannot be repeated?

• (26*3)+(10*3)

• $$36^6$$  

• 36*35*34*33*32*31

Multiple Choice

How many student ID numbers can be made by 4 random digits (zero cannot come first) followed by the student’s grade (9, 10, 11 or 12).

Example: 5422-12 for a grader.

• 40,000

• 36,000

• 108,000

• 9000

Multiple Choice

How many different three scoop cones can be made from 12 flavors of ice cream allowing for repetition? What if no flavors can be repeated?

• 36; 1320

• 20736; 324

• 1728; 36

• 1728; 1320

Multiple Choice

How many five digit numbers can be formed that end in 5 and the digits cannot be repeated?

• 5040

• 3024

• 6561

• 6561

Multiple Choice

How many license plates can be formed of 2 letters followed by 2 numbers, if the letters and numbers cannot be repeated ?

• 58,500

• 67,600

• 65,000

• 60,840