audreynw420
Answered

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I'm trying to figure this out for extra credit but I don't know what to do can someone step by step take me through it with the answer?​

Im Trying To Figure This Out For Extra Credit But I Dont Know What To Do Can Someone Step By Step Take Me Through It With The Answer class=

Sagot :

sqdancefan

Answer:

  2800

Step-by-step explanation:

The choice at any node (except the edges) is to go right or go down.

A to B

To get from A to B requires a total of 4 choices to go down, and 4 choices to go right. Those can occur in any order. Locating the "right" choices in the list of "all" choices is effectively choosing 4 of 8. The number of ways those choices can be made is ...

  C(8, 4) = 8!/(4!(8-4)!) = 8·7·6·5/(4·3·2) = 70

B to C

Similarly a total of 2 choices must be made, 1 of which is a "right" choice. The number of ways those can be ordered is ...

  C(2, 1) = 2 . . . . . . . that is: (right, down) or (down, right)

C to D

A total of 6 choices must be made, of which 3 are "right." The number of possible orderings is ...

  C(6, 3) = 6·5·4/(3·2·1) = 20

Total paths

Each set of choices is independent of the others, so the total possible number is the product of the numbers of choices on the subpaths:

  total paths = (70)(2)(20) = 2800

There are 2800 possible paths from A to D.

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