haha combinations! (1 Viewer)

[Smilebuffalo]

Hey guys... again.... I finished the permutations exercise thanks to all the help you guys provided. But now i'm doing combinations and i'm bad at this too.

Anyway these are the questions i couldn't get correct so far....


7. A committee of 6 is to be selected from 10 people of whom A and B are two. How many committees can be formed excluding A if B is included? (answer = 140)

8. In how many ways can 3 cards be selected from a pack of 52 cards if:
i) at least one of them is an ace? (answer = 4804)
ii) not more than one is an ace? (answer = 21,808)

 

[Timothy.Siu]

Hey guys... again.... I finished the permutations exercise thanks to all the help you guys provided. But now i'm doing combinations and i'm bad at this too.

Anyway these are the questions i couldn't get correct so far....


7. A committee of 6 is to be selected from 10 people of whom A and B are two. How many committees can be formed excluding A if B is included? (answer = 140)

8. In how many ways can 3 cards be selected from a pack of 52 cards if:
i) at least one of them is an ace? (answer = 4804)
ii) not more than one is an ace? (answer = 21,808)

8i)no aces=48C3
52C3-48C3=4804
ii)48C3+4C1x48C2
(0 aces and 1 ace)

edit: totally misread the first quesiton

 

[gurmies]

7

Case 1 (B is included)

Since B is included, A must not be. You are now choosing 5 people from 8 = 8C5 = 56

Case 2 (A is included, meaning B cannot be)

Similarly, you are now choosing 5 people from 8 = 8C5 = 56

Case 3 (Neither A nor B included)

This is the same as choosing 6 people from 8, 8C6 = 28

2x56+28 = 140

8

i) This is the same as All combinations - no aces = 52C3-48C3 = 4804.

ii) This means either 0 aces or 1 ace.

For 0 aces, 48C3 = 17,296

For 1 ace 4C1x48C2 = 4,512

17,296+4,512 = 21,808

 

[Smilebuffalo]

for question 7... when i did it i only considered the number of possible commitees when B is included meaning A isn't. ie. 8C5 = 56.


How come i also have to consider when A is included and B isn't, and when neither A or B is included?


Oh wait nevermind what i just said i get it now. The question specifies IF B is included

Cool thanks a lot!