# Peak

Uphill leads 2 paths and 1 lift.

a) How many options back and forth are there?
b) How many options to get there and back by not same path are there?
c) How many options back and forth are there that we go at least once a lift?

Result

a) n =  9
b) n =  6
c) n =  5

#### Solution:

$n_a = (2+1)\cdot (2+1) = 9$
$n_b = (2+1) \cdot 2 = 6$
$n_b = 2 \cdot 1 + 1 \cdot 2 + 1\cdot 1 = 5$

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