Math question in DAT Destroyer

[MNova]

---

Members don't see this ad.

Hi guys,

I have the April 2008 version of DAT Destroyer.

Question #20 in QR states "How many ways can 8 horses finish a race in first, second and third place?"

A. 1
B. 6
C. 56
D. 336
E. 512

Question #27 in QR states "There are 12 members of the Democratic Party at a meeting. How many groups of 3 members can be formed?"

A. 20
B. 39
C. 110
D. 220
E. 1320

The answer to the first question is D, and it's solved by doing "n! / (n-r)!" which equals "8! / 5!"

The answer to the second question is D, and it's solved by doing "n! / [r! x (n-r)!]" which equals "12! / (3! x 9!)"

Can someone please explain when you have to include the r! in the denominator (as in the second question) and when you leave it out? Thank you!

 

[Talib]

Hi guys,

I have the April 2008 version of DAT Destroyer.

Question #20 in QR states "How many ways can 8 horses finish a race in first, second and third place?"

A. 1
B. 6
C. 56
D. 336
E. 512

Question #27 in QR states "There are 12 members of the Democratic Party at a meeting. How many groups of 3 members can be formed?"

A. 20
B. 39
C. 110
D. 220
E. 1320

The answer to the first question is D, and it's solved by doing "n! / (n-r)!" which equals "8! / 5!"

The answer to the second question is D, and it's solved by doing "n! / [r! x (n-r)!]" which equals "12! / (3! x 9!)"

Can someone please explain when you have to include the r! in the denominator (as in the second question) and when you leave it out? Thank you!

We use the first formula when order does matter in the question. it is asked to find # of ways 1st, 2nd and 3rd. it is called the permutaion formula: n! / (n-r)!

We use the second one when order does not matter in the question ( any 3 groups out of 12). it is called the combination formula: n! / [r! x (n-r)!]

Hope this will help you,

 

[eat2123]

Thanks Talib. That helps a lot. I've been wondering about that also.

 

[Talib]

u r welcome. we just had a tornado warning !!! something else to not put me in the mood to study 🙂

 

[MNova]

u r welcome. we just a tornado warning !!! something else to not put me in the mood to study 🙂

Perfect, thank you so much!

 

[MNova]

Based on the advice above, I thought I understood the difference. But, maybe not. Can someone explain to me why the following question in Destroyer uses the formula that is reserved for when "order does matter?"

#86: "A house has 4 rooms, and a painter has 9 colors. If hte rooms are A, B, C, and D, how many different ways can he paint the rooms?"

According to the solution manual, the answer is:

9! / (9-4)! = 3024

I guess I'm having difficulty understanding why "order" would matter here.

Any help would be appreciated!

P.S. In questions such as above, how do you know if you're allowed to repeat a color? If so, isn't there a different equation for that? I found this equation on line for when you can repeat:

(n + r - 1)! / [r!(n-1)!]

Geez.