A Street has 13 houses in a row as shown in the figure. Some residents in the first
house tested positive for COVID-19. The virus spreads in two ways: it can spread to
the next house, or jump directly to the third house. Residents of house number 2 can
get infection in only one way, the house number 3 in two ways, the house number 4
in 3 ways, the house number 5 in 5 ways and so on. If the virus only progresses from
Left to Right direction, in how many ways can the residents of the house number 13
get infected?
Answers
Step-by-step explanation:
2nd by one way..
3rd by 2way
4th by 3way
5th by 5 way
6th by 8 way
7th by 13 way
8th by 21 way
9th by 34 way
10th by 55way
11th by 89 way
12th by 144way
13th by 233 way
233
Step-by-step explanation:
As we can see the series of spreading is
House Ways
1 1
2 1
3 2
4 3
5 5
From this we can see that House number x is affected by addition of ways of house number (x-1) and house number (x-2).
So, lets make a table.
House Ways
1 1
2 1
3 2
4 3
5 5
6 (3+5)=8
7 (5+8)=13
8 (13+8)=21
9 (21+13)=34
10 (34+21)=55
11 (55+34)=89
12 (89+55)=144
13 (144+89)=233
Therefore, there are total 233 ways in which House number 13 can get affected.