Question

1. permutation or combination: how many schedules are possible if you need to choose 5 events out of 20 for a vacation?

Is it permutation?? Answer is 1860480?

2. a. How many area codes are possible ( the 3 digit number can't start with a 0)?
504?
b. How many area codes start and end with an even number?
84?
c. How many area codes have 5 as the middle number?
56?

3. In the word "TIGARD", how many 3 letter words ( repeats not allowed)
a. start with a vowel? 40?
b. are all consonants? 24?
c. are all vowels? 0?
If repeats are allowed, how many consonant words are there for the previous question?
64?

Answer 1

1. NO
The order does not matter, Disney first or white mountains first
so
COMBINATION C(20,5)

Answer 2

c(20,5) = 20!/(5!*15!)

= 20*19*18*17*16 /(5*4*3*2)

= 15504

Answer 3

2a 9*10*10 = 900

2b 4 * 5 * 5

2c 9 * 1 * 10

Answer 4

6 letters
if start with A so 5 left
c(5,3) = 10
10 more start with I so
20 total

others similar

Answer 5

#3
Those are permutations since the order matters

a) start with a vowel:
2*5*4 = 40 , you were right

b) all consonants, means we only pick from 4
4*3*2 = 24 , you were right

c) all vowels, you are right with 0
since we only have 2 vowels and we need 3

d) all consonants , repetition allowed:
4*4*4 = 64 , again you were right.