Question

FIFTY POINTS!! Please help! I'll give brainliest

Answer 1

Answer:

4851 ways

Step-by-step explanation:

The fish have 3 choices. They can make it above, below, or though the pipe. Keep in mind there are 100 fish total:

group 1 + group 2 + group 3 = 100

If we keep group 3 (the fish that swim below the pipe) constant, say 1, and increment the other two (group 2 starting off at 1) we find 98 possibilities.

   98     +      1        +      1        = 100,

   97      +     2        +      1        = 100,

   96      +     3        +      1       =  100

        .           .            . 98 possibilities

Now we take group 1 as one greater (1 + 1 = 2) and then start incrementing group 2 starting from 1 as done before. So 97 + 2 + 1 = 100. Followed by 96 + 3 + 1, 95 + 4 + 1...97 possibilities

If we continue this pattern, we have 98 + 97 + 96... + 1 total possibilities to partition this school of fish.

98 + 97 + 96... + 1,

Sum = n(n + 1)/2 = 98(98 + 1)/2 = 98(99)/2 = 4851