The gardener must plant 6 trees within three days. In how many ways can he distribute the work over the days if he plants at least one tree a day?

Suppose a gardener plants trees in a row and can make different decisions about which tree to stop after on the first day and after which on the second. Thus, one can imagine that the trees are separated by two partitions, each of which can stand in one of 5 places (between the trees). The partitions should be there one at a time, because otherwise not a single tree will be planted some day. Thus, you need to select 2 elements out of 5 (no repetitions). Therefore, the number of ways C2 5 = 10.

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