Hey guys, I'm having some problems with combinations and permutations.

I have included my answers as well, explanations will be highly appreciated.

I'll try to give +rep+ if it is possible.

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1. The first three digits of a telephone exchange are 452.

If all the sequences of the remaining digits are equally likely, what is the probability that a randomly selected phone number contains seven distinct digits?

My answer:$\displaystyle \frac{7 \cdot 6 \cdot 5 \cdot 4}{10!} = \frac{1}{4320}$

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2. How many different meals can be made from four kinds of meat, six vegetables, and three starches if a meal consists of one selection from each group?

My answer:$\displaystyle \frac{13!}{4!6!3!} = 60 060$

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3. A woman getting dressed for a night out is asked by her significant other to wear a dress, high heeled sneakers, and a wig. In how many orders can she put on these objects?

My answer:$\displaystyle 3! = 6$

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4. Two dice are rolled, and the sum of the face values is six. What is the probability that at least one of the dice came up a 3?

My answer:$\displaystyle \frac{1}{6} + \frac{1}{6} = \frac{1}{3}$

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5. Answer problem 4 again, given that the sum is less than six.

My answer:Erm... Not sure. Maybe: $\displaystyle 1 - 0,333 = \frac{2}{3}$ ?

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6. A couple has two children. What is the probability that both are girls given that the oldest is a girl? What is the probability that both are girls given that one of them is a girl?

My answer:Isn't that the same thing? One is always a girl?

$\displaystyle \frac{1!}{2!} = 0,5$

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7. A box has three coins. One has two heads, one has two tails, and the last is a fair coin with one head and one tail. A coin is chosen at random, is flipped, and comes up heads.

a) What is the probability that the chosen coin is the two headed coin?

b) What is the probability that if it is thrown another time it will come up heads?

c) Answer part a) again, supposing that the coin is thrown a second time and comes up heads again.

My answers:

a) $\displaystyle \frac{1!}{2!} = 0,5$ (Not sure about this one though...)

b) If it's the fair coin, 50%

....If it's the two headed one, 100%

But how do we tell???

c) Erm... Still 0,5?