Mar 10:45 For even the Son of man came not to be ministered unto, but to minister, and to give his life a ransom for many.
Alternative: Since even the Son of man set out not to be served but to serve and to give his breath in compensation for the sake of many.
This is the fourth and final verse emphasizing the idea of serving to lead, the theme of the chapter, in the pattern of three plus one. In this use of the pattern, the first iteration gives a counter principle, the second iteration, the general principle, the third the extreme principle, and the fourth an real example of the extreme, in this case, Christ. This can be mapped into the normal spiritual, mental, emotional, and physical form, but it requires the understanding the spiritual reverses the physical. In this case, since the subject is the spiritual reversal itself. The example of worldly leaders is a reversal of that reversal.
The most interesting word choice is the use of the word psuchê for "life." The word means the "breath of life," and specifically means the spirit that animates the body. For this reason, it is often translated as "soul" in the Gospels. The Gospels also translate another word, zôê, as "life," but that word has the sense of living as existence. When Christ uses the phrase translated as "eternal life" zôê is used.
The first "for" comes from gar (gar) which is the introduction of a clause explaining a reason or explanation: "for," "since," and "as." In an abrupt question it means "why" and "what."
"Come" is from erchomai (erchomai), which means to start," "to set out," "to come," "to go," and any kind of motion. It means both "to go" on a journey and "to arrive" at a place.
"Minister" is from diakoneô (http://www.blueletterbible.org/lang/lexicon/lexicon.cfm?Strongs=G1247&t=KJV)">diakoneo), which "to act as a servant," "to minister," and "to perform services."
"Give" is from didômi (didomi), which means "to give," "to grant," "to hand over," and "to describe."
"His" is from autos (autos), which means "the same," and the reflexive pronouns, "myself," "yourself," "himself," "herself," "itself," or the oblique case of the pronouns, "him," "her," and "it." It also means "one's true self," that is, "the soul" as opposed to the body and "of ones own accord."
"Life" is from psuchê (psyche), which means "breath," "life," "self," "spirit," and "soul." It has the clear sense of the conscious self. It is also used to describe "the spirit" of things. It is often translated as "soul."
"Ransom" is from lutron (lytron), which means "ransom," "sum paid for the redemption of a pledge," "atonement," and "recompense."
The second "for" is from anti (anti) which means "opposite," "over against," "instead," "in place of," "at the price of," "in return for," "at the price of," "for the sake of," "against," "in return," "equal to," "corresponding to," and "mutually."
"Many" is from polus (polys)," "great (in size or power or worth)," and "large (of space)." As an adverb is means "far," "very much," "a great way," and "long."