Conjecture Let x and y be integers. If x is even and y is odd, then xy is even. Try some examples. Does the conjecture seem to be true or false?

SOLVE ONLY FOR (L) (M) AND (O)

File Preview A gardener has ten different potted plants, and they are spraying the plants with doses of Tertizers. Plants can receive zero or more doses in a session. In the following, we count each possible number of doses the ten plants can receive (the order of spraying in a session does not matter). (a) How many ways are there if there were twelve total doses of a single type of fertilizer? (b) How many ways are there if there are six total doses of a single type of fertilizer, each plant receives no more than one dose? (c) How many ways are there if is was one dose of each of six types of fertilizers? (d) How many ways are there if there are four doses of fertilizer #1 and eight doses of fertilizer #2? (e) How many ways are there if there are four doses of fertilizer #1 and eight doses of fertilizer #2, and each plant receives no more than one dose of fertilizer #1? (f) How many ways are there to do two sessions of spraying, where each plant receives at most two doses total?