It is currently 17 Oct 2017, 12:16

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Intern
Joined: 08 May 2003
Posts: 5

Kudos [?]: [0], given: 0

Location: San Francisco

### Show Tags

23 May 2003, 12:21
Hi,
I was unable to solve these 3 problems from your probability lesson, please can you help me:

3. How many different signals can be transmitted by hoisting 3 red, 4 yellow and 2 blue flags on a pole, assuming that in transmitting a signal all nine flags are to be used? (Ans. 1260)

I would say that it should be done as a problem where you have to find combinations of different words that can be formed from 9 letters where 3 letters A, 4 letters B and 2 letters C. In this case it should be 9!/(3!*4!*2!), but I do not fully understand a logic behind this?

2. There are 5 married couples and a group of three is to be formed out of them; how many arrangements are there if a husband and wife may not be in the same group? (Ans. 80)

There are C(10,3)=120 combinations, minus combinations when there is a husband and a wife in a group of three: 5(5 different couples)*8(8 choices for one more place in a group)=40. Total 120-40=80. Is it a right approach?

7. The probability that it will rain in NYC on any given day in July is 30%. What is the probability that it will rain on exactly 3 days from July 5 to July 10 ?

There are C(5,3)=10 desired combinations of rain in 3 days and it should be 32 possible combinations if probability of rain is 1/2, but we have probability of rain as 30%, i do not know what is the next step?

Thanks, Boris
_________________

Boris

Kudos [?]: [0], given: 0

Founder
Joined: 04 Dec 2002
Posts: 15568

Kudos [?]: 28475 [0], given: 5105

Location: United States (WA)
GMAT 1: 750 Q49 V42

### Show Tags

23 May 2003, 13:16
My comments are in BLUE...

Hi,
I was unable to solve these 3 problems from your probability lesson, please can you help me:

3. How many different signals can be transmitted by hoisting 3 red, 4 yellow and 2 blue flags on a pole, assuming that in transmitting a signal all nine flags are to be used? (Ans. 1260)

I would say that it should be done as a problem where you have to find combinations of different words that can be formed from 9 letters where 3 letters A, 4 letters B and 2 letters C. In this case it should be 9!/(3!*4!*2!), but I do not fully understand a logic behind this?

A good way to approach Permutations, etc is to build a model - a simple one. Take 4 flags total, 3 red and 1 blue and try to work with them. Basically, what you are doing by dividing 9! by 3!4!2! is you omitting the "internal" combinations - that is when the change happened within the 3 red flags, which is not noticeable. 3! is in how many ways you can arrange 3 different flags, but since our flags the same, all of these combinations have to be extracted (not subtracted since there is a number of other players - therefore division).

2. There are 5 married couples and a group of three is to be formed out of them; how many arrangements are there if a husband and wife may not be in the same group? (Ans. 80)

Here is a discussion about this topic; it was a pretty lengthy one; I hope it is clear. Post more if not.
http://www.gmatclub.com/phpbb/viewtopic.php?t=213&highlight=husband

There are C(10,3)=120 combinations, minus combinations when there is a husband and a wife in a group of three: 5(5 different couples)*8(8 choices for one more place in a group)=40. Total 120-40=80. Is it a right approach?

7. The probability that it will rain in NYC on any given day in July is 30%. What is the probability that it will rain on exactly 3 days from July 5 to July 10 ?

There are C(5,3)=10 desired combinations of rain in 3 days and it should be 32 possible combinations if probability of rain is 1/2, but we have probability of rain as 30%, i do not know what is the next step?

Here are explanations of this problem:

http://www.gmatclub.com/phpbb/viewtopic.php?t=100&highlight=rain

http://www.gmatclub.com/phpbb/viewtopic.php?t=705&start=0&postdays=0&postorder=asc&highlight=rain

http://www.gmatclub.com/phpbb/viewtopic.php?t=182&highlight=rain

Thanks, Boris

Kudos [?]: 28475 [0], given: 5105

Intern
Joined: 08 May 2003
Posts: 5

Kudos [?]: [0], given: 0

Location: San Francisco

### Show Tags

23 May 2003, 15:28
Thanks a lot for your help. The only problem that still is not 100% clear form me is a question about rain. This problem is resolved in 2 different ways:

1. P(3 rainy days and 3 nonrainy) = 0.3*0.3*0.3*0.7*0.7*0.7*20=0.18522

2. Probability of raining on three days in a five day period=5c3(0.3)(0.3)(0.3)(0.2)(0.2)

Why in second example we multiply by 0.2 and not by 0.7?

boris
_________________

Boris

Kudos [?]: [0], given: 0

Founder
Joined: 04 Dec 2002
Posts: 15568

Kudos [?]: 28475 [0], given: 5105

Location: United States (WA)
GMAT 1: 750 Q49 V42

### Show Tags

23 May 2003, 16:13
bobzilb wrote:
Thanks a lot for your help. The only problem that still is not 100% clear form me is a question about rain. This problem is resolved in 2 different ways:

1. P(3 rainy days and 3 nonrainy) = 0.3*0.3*0.3*0.7*0.7*0.7*20=0.18522

2. Probability of raining on three days in a five day period=5c3(0.3)(0.3)(0.3)(0.2)(0.2)

Why in second example we multiply by 0.2 and not by 0.7?

boris

Here is the correct answer: 6! / (6 - 3)!3! x 0.3 x 0.3 x 0.3 x 0.7 x 0.7 x 0.7 .

It is 6 days, so C(6,3)=20, which is the same as your answer #1. I am not sure about 0.2*0.2 I don't know where that came from and the answer does not match... probably somebody made a mistake

---

Kudos [?]: 28475 [0], given: 5105

23 May 2003, 16:13
Display posts from previous: Sort by

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

Moderator: HiLine

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.