An octagonal pyramid ... how many faces does it have, how many vertices and how many edges? A triangular prism ... how many face
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The Empire is attacking a Rebel base that is stocked with X-wings and
Y-wings. The Rebels need to build a fleet consisting of
ships (with at least 1 X-wing), to be led by 1 pilot in an X-wing.
There are ways of picking the leader, and
ways of building the rest of the fleet, so there's a total of
ways of building such a fleet.
In the other direction, suppose we build a fleet comprising of X-wings and
Y-wings. We have
ways of picking X-wings and
ways of picking Y-wings. Also from the
X-wings we pick 1 to be the leader, which we can do in
ways. So there are
ways of building such a fleet. But since
, we have
ways of building the fleet with these specifications. Sum over all possible values of ,