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PLEASE HELP... Students are making necklaces of six beads for their mothers. There are
six colours available. There is no clasp, so the necklace can be rotated.
The necklace can also be turned over.
In how many different ways can the students place the beads around the
necklace if exactly two colours are used?

Respuesta :

Answer:

Step-by-step explanation:

#1 Number of ways picking 2 from 6 = 6C2 = 15

#2 Arranging them in a circle (consider 1 pair AB)

can be done

1,5  (ABBBBB)   or (5,1)

2,4 ( AABBBB) or (4,2)

3,3

1,1 (ABABAB)

all up = 7 ways

#3 = product of #1 and #2 = 15x7 = 105