7 people are attending a concert.
(a) In how many different ways can they be seated in a row?
(b) Two attendees are Alice and Bob. What is the probability that Alice sits next to Bob?
(c) Bob decides to make Alice a rainbow necklace with 7 beads, each painted a different colour on one side (red, orange, yellow, blue, green, indigo, violet), placed on a chain that is then closed to form a circle. How many different necklaces can he make? (Since the beads can slide along the chain, the necklace with beads R O Y G B I V would be considered the same as O Y G B I V R for example. The beads are plain on the back, so the necklace cannot be turned over.)
How should i approach these questions? Are they correct?
for the first one i understand that it is a permutation. Therefore would a) = 7! = 5040 possible different ways of sitting in a row
b) p(7,2) = 7!/(7-2)! = 5040/120 = 42 therefore probabiltiy = 42/5040 = 0.0083%
c) =6!/2 because the first bead doesnt matter and over 2 as it can either go left or right.