Question

A deli makes potato, macaroni, three bean, Caesar, 7-layer, and Greek salads. The deli randomly makes only four salads each day. What is the probability that the four salads made one day are 7-layer, macaroni, Greek, and potato?

Answer 1

The number of possible combinations are 7C4, since we are concerned about only one possible way to have "success," the probability is the reciprocal of that number. I.e.,\[\left(\begin{matrix}7 \\ 4\end{matrix}\right)=\frac{7!}{4!3!}=\frac{7*6*5*4!}{4!3*2}=35\]So the probability is 1/35.

Answer 2

wait.. for the denominator..do you mean:
four times three times two times one, then multiply it by three and two, which equals to six????
dat part was sorta confusing... :/

Answer 3

OOPs! Bad count on the number of salads. There are only six, so our number of combinations are 6C4, not 7C4 as I calculated above.

Answer 4

so it's six, not seven you mean, and wait.. for the denominator..do you mean:
four times three times two times one, then multiply it by three and two, which equals to six????
dat part was sorta confusing... :/

Answer 5

Hold on a second; let me do it correctly.

Answer 6

\[\left(\begin{matrix}6 \\ 4\end{matrix}\right)=\frac{6!}{4!2!}=\frac{6*5*4!}{4!*2}=15\]So the probability is 1/15.

Answer 7

Note that the 4!=4*3*2*1 is in both the numerator and denominator, so that factor cancels out. The 2! in the denominator is really just two.

Answer 8

When calculating this, we step the numerator only down to the largest factorial in the denominator, then cancel. This allows us to figure out the solution with the least work.

Answer 9

oh...wow...
OMFG, thanks, @animalain!!!!!!!

Answer 10

do...i...can..i...close this question now...er...?

Answer 11

Your call.....

Answer 12

okay...good night too you then.. and i think you teach college math or something...you told me...so um...get a good night's sleep, i suppose, and good luck on your...stuf.. :/)

Answer 13

THANKKKKK YOUUUUU!!!!!!!!!!!!!!!
<333