Combinations help (1 Viewer)

[iPhone4]

Hi all, could you help a fellow maths kid out here, I'm a bit stuck. All questions sourced from Fitzpatrick. I know the answers just not the steps to get there.

1) In how many ways can 3 cards be selected from a pack of 52 cards, if:
i) at least one ace is selected;
ii) not more than one is an ace?

2) A committee of 6 is to be selected from 10 people, of whom A and B are two. How many committees can be formed if:
i) A and B are both selected
ii) excluding A if B is selected

I got 2i, but not 2ii.

Thankyou very much

 

[braintic]

Hi all, could you help a fellow maths kid out here, I'm a bit stuck. All questions sourced from Fitzpatrick. I know the answers just not the steps to get there.

1) In how many ways can 3 cards be selected from a pack of 52 cards, if:
i) at least one ace is selected;
ii) not more than one is an ace?

2) A committee of 6 is to be selected from 10 people, of whom A and B are two. How many committees can be formed if:
i) A and B are both selected
ii) excluding A if B is selected

I got 2i, but not 2ii.

Thankyou very much

1. (i)
1 ace: 4C1 times 48C2
2 aces: 4C2 times 48C1
3 aces: 4C3
then add

(ii)
0 aces: 48C3
1 ace: 4C1 times 48C2
then add

2. (i) 8C4

(ii) You can't have A and B together, so 10C6 minus previous answer

 

[namelyanonymous]

Different way to do i)
Total ways (including aces) - Total ways(without aces)
= 52C3 - 48C3 = 4804

 

[iPhone4]

New questions:

From 4 oranges, 3 bananas and 2 apples, how many selections of 5 pieces of fruit can be made, taking at least one of each kind?

How many ways can n things be shared between two people?

 

[HeroicPandas]

New questions:

From 4 oranges, 3 bananas and 2 apples, how many selections of 5 pieces of fruit can be made, taking at least one of each kind?

How many ways can n things be shared between two people?

First one: _ _ _ _ _
Pick one of each


Now there are 6 possible fruits to pick

so out of 6, choose 2



Second one:

ways = n(n-1)?

i might be wrong..