SOLUTION: There are 20 different pairs of shoes - 8 black pairs, 6 red pairs, 3 white pairs, 2 yellow pairs, and 1 brown pair . How many selections of 3 pairs of shoes are possible if at lea

Question 1117931: There are 20 different pairs of shoes - 8 black pairs, 6 red pairs, 3 white pairs, 2 yellow pairs, and 1 brown pair . How many selections of 3 pairs of shoes are possible if at least 1 pair of shoes is black?
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.

I will assume that the word "different" is applicable UNIFORMLY to all and each pairs/pair, literally as the condition says it.

Thus each pair is considered as DISTINGUISHABLE and individual.

Then the way to solve the problem is THIS:

     First find the number of ALL POSSIBLE selections of 3 pairs 

     and then subtract all the selections NOT CONTAINING any black pair.

Solution

1.  The number of all possible selections of 3 pairs (disregarding the color) is

        20*19*18 = 6840.



2.  Without 8 black pairs, there are 20-8 = 12 other pairs,

    and the number of selections of 3 pairs among these 12 pairs is

        12*11*10 = 1320.



3.  Thus the number under the question is the difference  6840 - 1320 = 5520.



Answer.  There are 5520 selections satisfying to the problem's requirements.

RELATED QUESTIONS
A shoe store sells 4 pairs of black shoes for every 7 pairs of brown shoes. there were... (answered by lashae_dee)

Tom has 8 shirts, 3 pairs of jeans, and 4 pairs of tennis shoes. How many different... (answered by rfer)

8.You randomly pick a pair of socks from the drawer, which contains 2 pairs of BLUE... (answered by jorel555)

Awomanhasawardrobecontaining5hats(red,bluegreen,blackandwhite),3pairsofslacks(black, blue (answered by ikleyn)

Awomanhasawardrobecontaining5hats(red,bluegreen,blackandwhite),3pairsofslacks(black,... (answered by ikleyn)

A woman has award robe. containing 5.... (answered by Boreal,solver91311)

you have 3 pairs of pants , 4 shirts, and 2 pairs of shoes to choose from in the morning. (answered by ikleyn)

A student has 3 different shirts, 2 different pairs of pants, and 4 pairs of shoes. How... (answered by rfer)

There are three shirts, five pairs shorts, and two pairs shoes. How many different... (answered by edjones)