Question:

There are 8 opposite-sex married couples at a party. Two people are chosen at random to win a door prize.

a) What is the probability that the 2 people will be married to each other?

My answer: n(S) = (16 2) n(E) = ( 8 1)

P(married couple chosen) = (8 1) ÷ (16 2) = 8/20 = 1/15

Therefore, the probability is 1/15.

c) If 6 people are chosen, what is the probability that they are 3 married couples?

My answer: n(S) = (16 6)
n (E) = (8 3)

Therefore, P(3 married couples chosen) = (8 3)÷ (16 6) = 56/8008 = 7/1001
Thus, the probability that the 6 people chosen will be 3 married couples is 7/1001.

2. ## Probability

Hello cnmath16

Looks good to me, apart from your typo in (a): should be 8/120 = 1/15; and in (c) the answer cancels to 1/143.

3. Hello, cnmath16!

And thank you for showing us your work!

As Grandad pointed out: . $\frac{7}{1001} \:=\:\frac{1}{143}$

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

A bit of trivia to keep in mind: . $1001 \:=\:7\times11\times13$

This is the basis for a mathematical trick.

Decide in advance whether you want your volunteer to get a Lucky or Unlucky number.

Lend him a calculator and stand some distance from him.

Instruct him to select any three-digit number mentally.
Have him enter his number twice, forming a six-digit nunber.

From across the room, you "concentrate" on his number.
Then you announce that he selected a very lucky (or unlucky) number.

You add that his number just happens to be divisible by eleven.
Have him divide by 11.

You "concentrate" on his new number.

If he is to be Lucky, say that his number just happens to be divisible by the unlucky 13.
. . To get rid of it, have him divide by 13.

If he is to be Unlucky, say "Too bad, your number is divisible by the lucky 7.
. . We have to get rid of it." .Have him divide by 7.

"Concentrating", you say that it is divisible by his original three-digit number.
Have him divide by it.

Ask him for his final answer.. . It will be 7 or 13.

And you can say, "See? I told you that it was a Lucky (or Unlucky) number."

I assume you can figure out why this works.
.