Red and blue beads are being strung to make a bracelet. How many different bracelets can be formed it each bracelet uses exactly 5 beads?
Visualize the beads on a string stretched out in front of you
Cases:
A) all blue --- one way
B) 1 red, 4 blue:
number of choices = 5!/(1!4!) = 5
e.g.
RBBBB, BRBBB, BBRBB, BBBRB, BBBBR
BUT... RBBBB and BBBBR are really the same bracelet, merely flipped, so there are really only 3 of these
C) 2 red, 3 blue
number of choices = 5!/(2!3!) = 10
again , 5 of those are symmetrical, so only 5 of these
D) 3red, 2 blue
same as C), --- so 5 of those
E) 4red, 1 blue
same as B), so 3 of these
F) all red ---- one of them
total = 1 + 3 + 5 + 5 + 3 + 1 = 18
check my thinking.
a bracelet is to be made from 2 red and 5 blue beads. how many different bracelets can be made
8. If all 5 beads are red, only 1 bracelet can be formed. If 4 beads are
red and 1 is blue, only 1 bracelet can be made. If 3 beads are red and 2 beads are blue, 2 different bracelets are possible: the blue beads together or separated by the red beads. The symmetry in this situation means that there will be 2 bracelets with 2 red and 3 blue beads, 1 bracelet with 1 red bead, and 1 bracelet with no red beads, for a total of 8 bracelets.
three
Blue=25 Red=30
To determine the number of different bracelets that can be formed using red and blue beads, we need to consider the combinations of the two colors in a sequence of five beads.
To solve this problem, we can use a combination formula. A combination formula is used when the order of the elements doesn't matter. In this case, we are selecting 5 beads out of a total of 2 colors (red and blue), so we can use the combination formula as follows:
C(n, r) = n! / (r! * (n-r)!)
Where n is the total number of colors (2 in this case), and r is the number of beads being selected (5 in this case).
Substituting the values into the formula:
C(2, 5) = 2! / (5!(2-5)!)
Simplifying further:
C(2, 5) = 2! / (5! * (-3)!)
Since the factorial of -3 is not defined, we can conclude that it is not possible to create different bracelets using exactly 5 beads with just two colors (red and blue).