Quiz 11

How many strings of length 10 over the alphabet {a, b, c, d} have at least one b somewhere in the string? Note: You do not have to give a final numerical value

Complement rule: # length 10 strings over the alphabet {a,b,c,d} - # length 10 strings over the alphabet {a,c,d} (no b's) = # length 10 strings with at least 1 b = 4^10-3^10

10 different movies will be stored on 40 computers such that each computer will have at most one movie. Since the movies are different, it matters which movie is stored on which computer. How many different ways can the 10 movies be stored? Note: You do not need to give a final numerical answer.

P(40,10)

A state's license plate has 7 characters. Each character can be a capital letter (A-Z), or a digit except for 0 (1-9). How many license plates are there in which exactly 3 of the 7 characters are digits? a) (7) * 9^3 * (26)^4 (3) b) (7) * (26)^4 (3) c) (7) * (35)^4 (3) d) P(7,3) * (35)^4

a) (7) * 9^3 * (26)^4 (3)

A class of 30 students with 14 boys and 16 girls must select 4 leaders. How many ways are there to select the 4 leaders so that at least one girl is selected? a) 16 * (29) (3) b) (30) - (14) (4) (4) c) 16 * (30) (3) d) (30) - (16) (4) (4)

b) (30) - (14) (4) (4)

How many ways are there to permute the letters in SOUPSPOONS? a) 10!/ 3!*2! b) 10!/ 3!*3!*2! c) 10!/ 3!*2!*2! d) 10!/ 3!*3!*2!*2!

b) 10!/ 3!*3!*2!

How many binary strings of length 10 have at least 2 adjacent bits that are the same ("00" or "11") somewhere in the string? a) 2^10 - 1 b) 2^10 c) 2^10 - 2 d) (2^10)/2

c) 2^10 - 2

20 applicants from a pool of 90 applications will be hired. How many ways are there to select the applicants who will be hired? a) 90^20 b) 20^90 c) P(90,20) d) (90) (20)

d) (90) (20)

There is a set of 14 jobs in the printer queue. Two of the jobs in the queue are called job A and job B. How many different ways are there for the jobs to be ordered in the queue so that job A is first or job B is last or both? a) 13! b) 2 * 13! c) 13! - 12! d) 2 * 13! - 12!

d) 2 * 13! - 12!