(a) Show that the number of paths from (0,0) to (n, m) taking steps of size (0,1) or (1,0) is (""). Show that the number of integer partitions (of any size) with at most n narts and with largest part of

A certain radioactive substance has a half-life of 3.6 years. Find how long it takes (in years) for the substance to decompose to 10% of its initial amount.

The booking limits for four fare classes in a flight are given as b = (b₁,b2, b3, b4) = (15, 10, 5, 2). (a) What is the available capacity for these four classes, i.e., what is the booking limit for classes {1, 2, 3, 4}? [ Select] (b) From this available capacity, how many seats are protected for class 1, i.e., what is the protection level for class 1? 15

-), Fuid the minimum to rhe consrant +3-22312, subfect using Lagrange Multipliers.