Mrs.Scale has 7 skirts,14 blouses and 3 sweaters. In how many ways can she choose 6 skirt,10 blouses and 2 sweaters to take on a trip? answer

Question

Mrs.Scale has 7 skirts,14 blouses and 3 sweaters. In how many ways can she choose 6 skirt,10 blouses and 2 sweaters to take on a trip? answer

Answer 1

This question requires using a kind of counting called "combinations", which allows us to find a number of combinations of n amount of r things. With combinations, the order of the things you choose doesn't matter. When the order of the chosen items matters (if you're choosing people out of a class to fill specific roles in the student government, for example) you use Permutations, not Combinations. TI graphing calculators have both under the MATH-->PROB menus. It's easy to do either by hand with the formulas too.

The number of ways to choose x things out of a group of y is often notated as _nC_r. C(n,r) is also common.

_nC_r = n!/[(n-r)!r!].

Remember that ! means "factorial", which is just multiplying a number by all the integers >0 and smaller than the number. So 3!=3·2·1=6. Calculators have factorial buttons, and they're easy to work with when dividing, since, for example, 100! / 99! = (100·99!) / 99! = 100. You can divide out any factorial expressions smaller than that in the numerator.

Back to your question, The way to choose 6 skirts out of 7 is C (6,7)= 7!/[(7-6)!6!]=7!/(1!6!)=7.

Use the same method for each along with the multiplication rule to find that Mrs. Scale has a possible

C(7,6)·C(14,10)·C(3,2) = 7·1001·3= 21,021 combinations!

I hope this helps, and let me know if you have any more questions.

Have fun mathing!

Liz Z.