A debate team has ten members

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1. A debate team has ten members. Five members must be chosen for a particular debate.
a.) In how many ways can the five be chosen if no positions are assigned to the members?
b.) In how many ways can the five be chosen if each member is assigned a position from one to five? The positions signify the order in which each member will participate in the debate.
c.) Suppose of the ten debate team members there are only two members who may be assigned position five in the debate. Any member may be assigned positions one through four. In how many ways can the five members be chosen?

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@D4ng1t,

a) This is the number of combinations of 10 objects taken five at a time. 10!/5!/(10-5)!
b) This is the number of permutations of 10 objects taken five at a time. 10!/(10-5)!
c) This is the number of permutations of 9 objects, taken four at a time times 2.

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A debate team has ten members

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