# Arrangement problem

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The number of distinct bracelets of five beads made up of red, blue, and green beads (two bracelets are indistinguishable if the rotation of one yield another) is,
a. 243
b. 81
c. 51
d. 47

Lets Solve this by patterns possible and there are

k!/(k−n)! ways to put k things into n ordered slots.

here k =3 and n ordered slots can understood as:

RRRRR here all beads of red color so it is 1 ordered slot

RRBBR here there are 2 things used so it is 2 ordered slot.

Now Let R =x, G=y, B=z

possible combinations

xxxxx: 3 = 3!/(3−1)!

xxxxy: 6 = 3!/(3−2)!

xxxyy: 6 = 3!/(3−2)!

xxxyz: 6 = 3!/(3−3)

xxyyz: 6 = 3!/(3−3)!​​​​​​​

xxyxy: 6 = 3!/(3−2)!

xxyxz: 6 = 3!/(3−3)!

xxyzy: 6 = 3!/(3−3)!

xyzyz: 6 = 3!/(3−2)!

3 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 = 51

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The number of ways, we can arrange 5 books in 3 shelves ________. Given answer 2520 n=3 r=5 so answer is 3-1+5 P5= 7p5= 2520 My answer 3*3*3*3*3= 243 Where am I doing wrong? please help