help with combinationss (1 Viewer)

[nick90]

Gday everyone, I'm having a few problems with understanding combinations - it's very frustrating! I was wondering if you can help me with understanding some of these problems from the fitzpatrick textbook.

Ex 28 (b)

Q 8: In how many ways can 3 cards be selected from a pack of 52 playing cards if (i) at least one of them is an ace?


I can't understand why in (i) you can't just go 4C1 x 51C2 ? I eventually worked out the correct answer another way, but I don't understand why 4C1 x 51C2 doesn't work.


Q 10: A committee of 7 politicians is chosen from 10 liberal members, 8 labor members and 5 independents. In how many ways can this be done so as to include exactly 1 independent and at least 3 liberal members and at least 1 labor member?


I just have no idea how to approach this one.

Any and all help is appreciated! Thanks.

 

[denoz]

For question 10:

(5 x 10C3 x 8C3) + (5 x 10C4 x 8C2) + (5 x 10C5 x 8C1) = 73080

 

[alez]

lol i did those exact questions. anyway

ok question 8 u have to work out whether its 1,2 or 3 aces separately.

1 ace - 4C1 X 48C2 =4512
2 ACE - 4C2 X 48C1 = 288
3 ACE - 4C3 = 4
total = 4804

u cant just go 4C1 cuz u have to work out how many u can. 4C1 is just one set of possibilities. it says at least so u have to work out 1,2 or 3 aces

10 - i draw up tables with all the possibilities its easier and then work it out

ind lib lab
1 3 3
1 4 2
1 5 1

this way its easier to see what u have to work out. 5C1 X 10C3 X 8C3 for the first one and then add all answers up

 

[nick90]

thanks a lot for the help with that. I think it's helped my understanding a fair bit.


Cheers