Probability Q

prachi18oct wrote:There are 7 ingredients at a salad bar that are available for creating salads: romaine lettuce, field greens, cherry tomatoes, cucumbers, squash, spinach, arugula, and bell peppers. Patrons at the salad bar are permitted three servings of any topping. If a patron chooses three servings, what is the likelihood that those servings will be spinach, cherry tomatoes, and cucumbers?
A 1/840
B 1/343
C 6/343
D 2/35
E 34/35

Does order matter here? I dont think it should but the OA points as if order does matter.
Please explain

Hi prachi18oct,

Could you please confirm that there is no error in the post- The answer choices look weird!?

Thanks.

The options given are as in the question

[spoiler]B?[/spoiler]

bubbliiiiiiii wrote:[spoiler]B?[/spoiler]

How did you arrive at this answer?

He has done probably 1/7*1/7*1/7
but my question is that the order matter here?
It can be in any order according to me and so it should be arranged in 3! ways leading to 6/343

Experts pls share your thoughts

prachi18oct wrote:He has done probably 1/7*1/7*1/7
but my question is that the order matter here?
It can be in any order according to me and so it should be arranged in 3! ways leading to 6/343

Experts pls share your thoughts

That's correct. Those 343 arrangements include 3! = 6 permutations of the three choices specified. So you need to divide 6 by 343 to get the answer.

In case it's not clear to anyone reading this, here's how to get the answer.

We have three slots. _ _ _

Each slot can be filled in 7 ways. So to find how many different ways there are to fill the slots we multiply 7 x 7 x 7 = 343.

The thing is that many of those 343 arrangements are effectively the same salads. A salad made by first choosing cucumbers, then choosing squash and finally choosing spinach is effectively the same as one made by choosing first spinach, then cucumbers then squash.

So the salad made with the specified three ingredients shows up multiple times in the 643 different arrangements. How many times? Well 3 ingredients can be arranged 3! = 6 ways.

So the specified salad shows up 6 times in the 343 different arrangements and the probability of its being selected is therefore 6/343.