the positive integer 4 can be represented as a sum of 1s or 2s in five ways?

Question

the positive integer 4 can be represented as a sum of 1s or 2s in five ways,such as 1+2+1 and 1+1+2.in how many ways can the positive integer 5 be represented as a sum of 1s or 2s?

Answer 1

1+1+1+2
1+2+1+1
2+1+1+1
1+1+2+1
1+2+2
2+1+2
2+2+1

Ans, 7 ways
:-)

Answer 2

8 ways:
1+1+1+1+1
1+1+1+2
1+1+2+1
1+2+1+1
2+1+1+1
1+2+2
2+1+2
2+2+1

Answer 3

2+2+1
2+1+2
1+2+2
2+1+1+1
1+2+1+1
1+1+2+1
1+1+1+2

Answer 4

There are only two sets that can produce arrangements resulting in a sum of five. The sets are: {1, 1, 1, 2} and {1, 2, 2} given that you can only use 1 and 2.

Suppose that order is important, then we have 24 possible arrangements for {1, 1, 1, 2} and 6 possible arrangements for {1, 2, 2}. In other words 30 (24+6) ways. However, if order is not important, then we have 24/3! for the set {1, 1, 1, 2} and 6/2! for the set {1, 2, 2}.
In other words a total of 4+3 or 7 ways.

You can devise a general solving procedure for this sort of problem as follows:

1. You write down the possible sets.
2. For each set, you calculate n!/s! where n is the number of elements in each set and s is the number of elements that are the same. Call this value t.
3. Add all the t values for each set and this will represent the total number of ways.

Answer 5

For 4, in 5 ways:
1:2+2
2:1+1+2
3:1+2+1
4:2+1+1
5:1+1+1+1


For 5 in 8 ways:
1:1+2+2
2:2+1+2
3:2+2+1
4:1+1+1+2
5:1+1+2+1
6:1+2+1+1
7:2+1+1+1
8:1+1+1+1+1

Answer 6

8 ways
1+1+1+1+1
1+1+1+2
1+1+2+1
1+2+1+1
2+1+1+1
2+2+1
2+1+2
1+2+2

:)

Answer 7

1 + 1 + 1 + 1
1 + 1 + 2
2 + 1 + 1
1 + 2 + 1
2 + 2

5 ways

-------------------------------------------------

1 + 1 + 1 + 1 + 1
1 + 1 + 1 + 2
1 + 1 + 2 + 1
1 + 2 + 1 + 1
2 + 1 + 1 + 1
2 + 2 + 1
2 + 1 + 2
1 + 2 + 2

8 Ways

Answer 8

1+1+1+1+1 (1 way)
1+1+1+2 (4 ways)
1+2+2 (3 ways)

8 ways

Answer 9

1+1+1+1+1
1+1+1+2
1+1+2+1
1+2+1+1
2+1+1+1
2+2+1
2+1+2
1+2+2

i've got 8 so far

Answer 10

1+1+1+2
1+1+2+1
1+2+1+1
2+1+1+1
1+2+2
2+1+2
2+2+1

Ans, 7 ways.