Posted by **kitkat** on Saturday, November 27, 2010 at 10:03pm.

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 -
**Reiny**, Saturday, November 27, 2010 at 11:28pm
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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