Hello, janvdl!

There are 10,000 possible four-digit numbers (from 0000 to 9999).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?

Since 4, 5, and 2 are already used, there are seven digits available.

. . The first digit can be any of the 7 available digits.

. . The second digit can be any of the 6 remaining digits.

. . The third digit can be any of the 5 remaining digits.

. . The fourth digit can be any of the 4 remaining digits.

Hence, there are: . numbers with seven distinct digits.

Therefore: .

Number of meals is: .2. How many different meals can be made from 4 kinds of meat, 6 vegetables,

and 3 if a meal consists of one selection from each group?

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:. . . . Right!

We are told that sum is six.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?

There were five possible outcomes: . 2,4),\3,3),\4,2),\5,1)" alt="(1,5),\2,4),\3,3),\4,2),\5,1)" />

Among them only one has a "3".

Therefore: .

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

There are eleven possible outcomes:

. .

Among them, four of them contain a "3".

6. A couple has two children.

(a) What is the probability that both are girls given that the oldest is a girl?

(b) What is the probability that both are girls given that one of them is a girl?

(a) The oldest child is a girl.

The probability that the younger child is also a girl is

That is: .

(b) This is a classic trick question.

We are told thatoneof the children is a girl.

Then there arethreepossible cases . . .

[1] The older is a boy, the younger is a girl.

[2] The older is a girl, the younger is a boy.

[3] Both are girls.

Among the three cases, only one has two girls.