Hi, I came across the following questions in a series of GMAT permutation questions, and they stumped me (either I couldn't figure them out, or I thought the proposed answer was wrong):

1. In how many ways can 5 people sit in a circle:
1) without any restrictions: got this (5-1)!
2) one should not have the same neighbors in any two arrangements: not sure about this, but have 4! - 3*5 = 9

2. In how many ways can 5 identical black balls and 7 identical white balls be arranged in a row so that no two black balls are together:
A) 56
B) 64
C) 65
D) 316
E) 560
The answer key says A, but I'd like to understand the mechanism

3. In how many ways can one choose 6 cards from a normal deck of cards so as to have all suits presents:
A) 13^4 * 48 * 47
B) 13^4 * 24 * 47
C) 48 Choose 6
D) 13^4
E) 13^4 * (48 Choose 6)
The answer key says B, but I worked it out and A makes more sense

4. How many numbers greater than a thousand can be made using the following digits without repetition: 1, 0, 3, 4, and 5:
A) 96^2
B) 96*2
C) 576
D) 24^2
E) 24*96
This one makes no sense to me, the answer may have been written incorrectly, because any combination of these digits will be greater than a thousand, even if we start with 0, so my answer would have been 5!=120

5. A mocktail has to be prepared from three kinds of whiskey, 4 kinds of soda and five kinds of fruit juice. How many mocktails can be made taking at least one of each kind?
A) 235
B) 325
C) 3255
D) 5235
E) 565
Again, another example of a poorly written question. From the question stem, what other possibilities are there other than multiply the choices through, i.e. 3*4*5 = 60, which is not an answer option

Any guidance would be good. Thanks!

Aren't Mocktails non alcoholic

Anyways, in your solution you considered one of each kind instead of at least 1 of each kind. I am still trying to figure out the answer.
_________________

Rock On

Atish why don't you try normal permutation method
4 digit nos = 4*4*3*2 = 96
5 digit nos = 4*4*3*2*1 = 96
total possible nos = 96*2...OA B
_________________

Bhushan S.
If you like my post....Consider it for Kudos

Define normal permutation method , I don't see permutations in your answer, just a bunch of factorials and multiplications with minimal explanation.
If there is a predefined formula for such questions I am all ears. Does it take 0 and non 0 numbers into account?

Appreciate your advice.
_________________

Rock On

Could you plz explain question 2?

Thanks a lot MBAhereIcome
BTW, how was your test? I see you mentioned that your GMAT test was supposed to be on 10-31-2011