Math Help Permutations and Combinations!!?

Question

In Morse Code all characters are transmitted using a sequence of four symbols, each of which with a dot or a dash?

(a) How many different characters can be forme with a sequence of fousr symbols, each which is a dot or dash?

(b) How many can be formed with a sequence of one, two, or three symbols?

I need help understanding how to do the problem the answers are 16 and14 I just need how to do it.

Answer 1

we note : 0 = dot & 1 = dash

(a)

2^4 = 16

0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111

(b)

one symbol : 2^1 = 2

0
1

two symbols : 2^2 = 4

00
01
10
11


three symbols : 2^3 = 8

000
001
010
011
100
101
110
111

(c)

2 + 4 + 8 + 16 = 30 solutions with 4 or less

Answer 2

a)2^4 =16 sequences.. there are two ways for the signal to be transmitted..2*2*2*2
b)for one symbol there are only 2 possibilities ;
two means 2^2=4 possibilities
three means 2^3=8 possibilities
total possibilities=2+4+8=14 ways

Answer 3

Part A
You have 4 places each with can be filled with one of two symbols, so you have 2 x 2 x 2 x 2 = 16 possible characters

Part B

You have 1 place each which can be filled with one of the two symbols, so you have 2 possible characters
You have 2 places each which can be filled with one of the two symbols, so you have 2 x 2 = 4 possible characters
You have 3 places each which can be filled with one of the two symbols, so you have 2 x 2 x 2 =8 possible characters

All together you have 2 + 4 + 8 = 14 possible characters

Answer 4

a)
How many choices do you have for the first symbol? (2)
for the second symbol? (2)
for the third? (2)
for the fourth? (2)

Answer is 2*2*2*2 = 16

b)
Using the same principle as above:
One symbol? 2
2 symbols? 2*2 = 4
3 symbols? 2*2*2 = 8

Total is 2 + 4 + 8 = 14