Question

3. Consider [5 letters of a, b, c, d, e' are taken 2 at a time, no repetition (25 pt.) (a) LIST all cases for permutations and determine permutations (number) (b) LIST all cases for combinations and determine combinations (number)

Answer 1

Page No.: Date —_I_ = { a, b, c, d, e } Elements of M taken 2 at a time Let us define convention caibas at first letter picked and b second lelta picked al Permutation Cases = 20 cases $ (a,b), (bia), Caic), cc,a2, caid), (dia) bie), (C,b), (bid), ( d, b), ( bre), ce,b), Cid),(dic), (C, e), (e, e), (die), (eid) Hare), Tera) items from a set of n items is given by Dlanin-nen-2) ----.3.2.1) a I Finding permutations of I np nl ?! m nami! Here na 5, mal , se 5) = 5 x4x3! = 20 pemutation 31 cb) For combinations (2,4)= 4x) - This is because anangement of items does not matter in combinations - Combination Cases - ca,b), caie), cald), caielo Teb,c), (b, d), (b, e), (eid) L Iecie), (bid) - 10 combinations. finding combinations of mitems from a set of nitems is given by cº n !_ nlenfu=171023)......327 (n-my!m! Hese ne sy mez_= P4-5! - 5x4831_=10 combinatione 3121 Cscal ned with CamScanner 31x2x)