Question

def: Let S = {al, a2, ..., an be a set. A word in S is a permutation of the elements in S. Five persons, A.B.C.D, and E, are going to speak at a meeting. a.) In how many orders can they take their turns speaking if B must speak (sometime) after A? b.) In how many orders can they take their turns speaking if B must speak immediately after A?

Answer 1

I I Five persons speak at A B a C D meeting E are going to a>. I In have turn (fometime many orders speaking i B after A can they must take speak IJ, A speaks first = 4! ways. = 24 ways The remaining 4 speakers can be arranged anyhow) If I speaks second = 3 x 31 = 18 ways. (The speaker before A can be one of C. D E. The remaining 3 speakers after A com be chosen in 31 ways) IJ A The 2 Where speaks 3rd before A B speaks = 3 + 2 x 2 = 12 ways can be chosen in 3x2 ways can be chosen in 2 ways). JJ A specks 4th = 3! = 6 ways The 3 speakers com be the ordered in 3! ways). de The final answer is = 24+18 + 12 +6 = 60 ways. by I В must speak immediately after A., Consider B AB as a single block. Now C, D, E AB can be argangel. -in. 41 = 24 ways In how many orders can they take their turns speaking if B must speak inmediately after A? 24 orders