Six tiles need to be placed in a row. There are 3 yellow tiles, 2 green tiles and 1 white tile. How many different patterns can be formed using all six tiles?
I'm assuming that the answer is not 6! because if you switch the yellow tiles around with each other, that does not make a new pattern.
I'm assuming that the answer is not 6! because if you switch the yellow tiles around with each other, that does not make a new pattern.
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(3+2+1)! / (3! * 2!) = 60
divide 6 ! by 3! and 2! because they are the number of ways the yellow and green tiles can be switched around themselves.
yyy gg w
yyy gwg
yyy wgg
y ggw yy
y gwg yy
y wgg yy
yy ggw y
yy gwg y
yy wgg y
ggwyyy
gwg yyy
wgg yyy
.....
there are already 12 cases before i even seperated ggw
it must be more than 14
divide 6 ! by 3! and 2! because they are the number of ways the yellow and green tiles can be switched around themselves.
yyy gg w
yyy gwg
yyy wgg
y ggw yy
y gwg yy
y wgg yy
yy ggw y
yy gwg y
yy wgg y
ggwyyy
gwg yyy
wgg yyy
.....
there are already 12 cases before i even seperated ggw
it must be more than 14
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14?
3^2 + 2^2 + 1^2
I beleive 60 is too many combinations. the 3 yellow are the same color so althugh moving them around is a new combination it does not make a new pattern. the same for the green. so your combinations are divided by the amount of identitcal tiles. 60 / 5.
3^2 + 2^2 + 1^2
I beleive 60 is too many combinations. the 3 yellow are the same color so althugh moving them around is a new combination it does not make a new pattern. the same for the green. so your combinations are divided by the amount of identitcal tiles. 60 / 5.