# Thread: Data Management Problem Help

1. ## Data Management Problem Help

I know I may be asking too much on this one, but please hear me out. I'm taking a data management course in summer school, summer school is only 3 weeks long. So basically, I'm learn a large amount of material everyday for six hours, material that would normally take a semester(5 months) to cover. So, as you may imagine, the pacing of the course is very quick.

So please sympathize with situation. I really need help with this problem.

Problem:

This is an organized counting problem.

a) In how many ways could you choose two fives, one after the other, from a deck of cards?

b) In how many ways could you choose a red five and a spade, one after the other?

c) In how many ways could you choose a red five or a spade?

d) In how many ways could you choose a red five or a heart?

a)12
b)26
c)15
d)14

2. Originally Posted by Morphayne
I know I may be asking too much on this one, but please hear me out. I'm taking a data management course in summer school, summer school is only 3 weeks long. So basically, I'm learn a large amount of material everyday for six hours, material that would normally take a semester(5 months) to cover. So, as you may imagine, the pacing of the course is very quick.

So please sympathize with situation. I really need help with this problem.

Problem:

This is an organized counting problem.

a) In how many ways could you choose two fives, one after the other, from a deck of cards?

b) In how many ways could you choose a red five and a spade, one after the other?

c) In how many ways could you choose a red five or a spade?

d) In how many ways could you choose a red five or a heart?

a)12
b)26
c)15
d)14
Ask your self are you picking with replacement and does order matter?
1) No and Yes (although the wording "one after another" took me a second - I think they mean that it matters).

Ok so you use combinations:

You want to pick 2 cards from 4. Even though there are 52 cards, it doesn't matter for this. You want to know how many ways to pick from the set of 5's.

${\mathbb{P}^4_2} = \frac{4!}{(4-2)!} = 12$

2) No and Yes

You want to pick 1 from 2 cards (2 red 5's) and then pick 1 from 13 cards (13 spades)

2*13 = 26

Technically you could do
${\mathbb{P}^2_1 * \mathbb{P}^{13}_1}$
but you get the same thing. It's just the more general approach.

3) Hint: This question is really asking (since you are only picking 1 card) how many cards satisfy (either red 5 or spade)?

4) Hint: This question is really asking (since you are only picking 1 card) how many cards satisfy (either red 5 or heart)? (notice that these sets overlap).