Suppose you have 5 beads: 1 yellow, 1 red, 1 blue, and 2 green, and you want to arrange them on a necklace. (Remember that the necklace can be rotated, so for example the order YRBGG is the same as the order BGGYR, and the necklace can also be flipped over, so the order YRBGG is the same as the order GGBRY.) How many unique ways can the beads be arranged on the necklace?
I did:
place B first, then decide arrangement of rest: 4!
this does not exclude the repeated letter G so divide 4! by 2! (number of ways G could be arranged)
4!/2! = 12 ways to arrange the beads
also:
If you have five friends A, B, C, D, E sitting in a row at a movie theater, how many ways can they be seated so that B is not sitting immediately to the right of C?
I did: 5! ways to sit them all
# of ways B is immediately right of C = 4!. So 5!-4! =96 ways
It seems too easy, can someone confirm I'm doing it correctly?
I did:
place B first, then decide arrangement of rest: 4!
this does not exclude the repeated letter G so divide 4! by 2! (number of ways G could be arranged)
4!/2! = 12 ways to arrange the beads
also:
If you have five friends A, B, C, D, E sitting in a row at a movie theater, how many ways can they be seated so that B is not sitting immediately to the right of C?
I did: 5! ways to sit them all
# of ways B is immediately right of C = 4!. So 5!-4! =96 ways
It seems too easy, can someone confirm I'm doing it correctly?