A person is standing at position (0,0) on an n by n grid. If she can only move in steps 1 unit up or 1 unit right, by ho

[answerhappygod]

A Person Is Standing At Position 0 0 On An N By N Grid If She Can Only Move In Steps 1 Unit Up Or 1 Unit Right By Ho 1 (22.08 KiB) Viewed 24 times

A person is standing at position (0,0) on an n by n grid. If she can only move in steps 1 unit up or 1 unit right, by how many paths can she reach the position (n,n)? For example, one valid path is n steps up followed by n steps right. Hint: Consider both the total number of steps and the total number of steps right.

You have been asked to assemble a two person task force from among your five person team.

a) How many such task forces are possible?

b) What if the task force consists of a designated leader and an assistant? n.5

c) You have been informed that exactly 2 members of your five person team are spies. How many of the task forces in part a include at least one spy?

d) With the above in mind, you have been given the discretion to pick as many members of your team for the task force as you would like (instead of exactly two). How many members must the task force include to ensure that at least one is not a spy? k25

= = Assume that ) = ("?) + (4=?) for n,k 2 1. Prove that for r, n 20, Eosken ("#") = (1+n+1). Hint: Use induction over n and the given formula. Feel free to answer on the back of this page.