In a packet of beads, 3/4 of the total beads are red in color. Namita uses 5/7 of the red beads to make bracelets. What fraction of the beads from the packet is used to make bracelets?
Answers
Answer:
Supposing all the 9 beads were to be of 9 different colors the number of ways to arrange them is 9! (9P9 = 9!/(9–9)! = 9!/0! = 9!/1 = 9!).
However we have 3 pairs of blue red and yellow beads and one triplet of green beads. In order to eliminate the same looking bracelets we need to eliminate them in the 9! bracelets. This we do by dividing 9! by (2!3!2!2!) to get the unique bracelets, which is 9!/(2!3!2!2!) = 7560
These 7560 unique ways are just linear arrangements and are not true bracelets. So we need to join the ends together to form a bracelets. When we do this by adding a clasp at the junction of two ends, then we get only half of 7560 bracelet designs. lets see what happens if we reverse, for example a particular brace let 2B3G2R2Y$ when reversed becomes 2Y2R3G2B$, where $ represents the clasp. Both are one and the same bracelet, as clasp is still between yellow and blue beads and the rest of the arrangement is also the same.
So we get 7560/2 = 3780 different baby bracelets.