# math 12

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Seven year-old Sarah has nine crayons; three blue, one red, two green and three yellow.
a) In how many ways can she line up the crayons on her desk?
b) She is to pick up some of the crayons. How many different choices of some crayons could she make?

• math 12 -

a) You should have a formula or procedure for that type of question
You are arranging n elements of which m are the same of one kine, k are the same of another kind, p are the same of another kind etc
number of ways = n!/(m!k!p!..)

so here number of ways to arrange the crayons
= 9!/(3!2!3!) = 5040

b) She can take the 3 blue crayons in 4 ways:
take none at all, take 1, take 2, take 3 or take 4
for each of those she can take the red crayons in 2 ways, the greens in 3 ways and the yellows in 4 ways
number of ways = 4x2x3x4 = 96 ways
BUT, that would include the single case of no crayons of any of the colours.
So final number of ways = 96-1 =95

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