Problem Solving

nahid078 wrote:The number of different signals which can be given from 6 flags of different colors taken one or more at a time is?

a) 1958
b) 1956
c) 1976
d) 1964
e) 1948

We'll need to handle each case separately.

# of 6-flag arrangements
stage 1: # of ways to select 1st flag = 6
stage 2: # of ways to select 2nd flag = 5 [since there are 5 flags remaining after the 1st flag is selected]
stage 3: # of ways to select 3rd flag = 4
stage 4: # of ways to select 4th flag = 3
stage 5: # of ways to select 5th flag = 2
stage 6: # of ways to select 6th flag = 1
By the Fundamental Counting Principle (FCP), we can complete all 6 stages (and thus create a 6-flag arrangement) in (6)(5)(4)(3)(2)(1) ways (=720 ways)


# of 5-flag arrangements
stage 1: # of ways to select 1st flag = 6
stage 2: # of ways to select 2nd flag = 5 [since there are 5 flags remaining after the 1st flag is selected]
stage 3: # of ways to select 3rd flag = 4
stage 4: # of ways to select 4th flag = 3
stage 5: # of ways to select 5th flag = 2
By the FCP, we can complete all 5 stages (and thus create a 5-flag arrangement) in (6)(5)(4)(3)(2) ways (=720 ways)


# of 4-flag arrangements
stage 1: # of ways to select 1st flag = 6
stage 2: # of ways to select 2nd flag = 5 [since there are 5 flags remaining after the 1st flag is selected]
stage 3: # of ways to select 3rd flag = 4
stage 4: # of ways to select 4th flag = 3
By the FCP, we can complete all 4 stages (and thus create a 4-flag arrangement) in (6)(5)(4)(3) ways (=360 ways)

We'll continue with the pattern to get....

# of 3-flag arrangements
(6)(5)(4) ways =120

# of 2-flag arrangements
(6)(5) ways =30

# of 1-flag arrangements
(6) ways =6

TOTAL number of arrangements = 720 + 720 + 360 + 120 + 30 = 6
= 1956

Answer: B

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Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch our free video: https://www.gmatprepnow.com/module/gmat-counting?id=775

Then you can try solving the following questions:

EASY
- https://www.beatthegmat.com/what-should- ... 67256.html
- https://www.beatthegmat.com/counting-pro ... 44302.html
- https://www.beatthegmat.com/picking-a-5- ... 73110.html
- https://www.beatthegmat.com/permutation- ... 57412.html
- https://www.beatthegmat.com/simple-one-t270061.html
- https://www.beatthegmat.com/mouse-pellets-t274303.html


MEDIUM
- https://www.beatthegmat.com/combinatoric ... 73194.html
- https://www.beatthegmat.com/arabian-hors ... 50703.html
- https://www.beatthegmat.com/sub-sets-pro ... 73337.html
- https://www.beatthegmat.com/combinatoric ... 73180.html
- https://www.beatthegmat.com/digits-numbers-t270127.html
- https://www.beatthegmat.com/doubt-on-sep ... 71047.html
- https://www.beatthegmat.com/combinatoric ... 67079.html


DIFFICULT
- https://www.beatthegmat.com/wonderful-p- ... 71001.html
- https://www.beatthegmat.com/ps-counting-t273659.html
- https://www.beatthegmat.com/permutation- ... 73915.html
- https://www.beatthegmat.com/please-solve ... 71499.html
- https://www.beatthegmat.com/no-two-ladie ... 75661.html
- https://www.beatthegmat.com/laniera-s-co ... 15764.html

Cheers,
Brent

sandipgumtya wrote:Brent sir/Mitch Sir,
I find this probability and P&C topic very terrifying.Can it hurt my score significantly?I have my exam scheduled next week.Can u plz help me with some last minute tips and tricks.

Thanks in adv.

Sandip.

I suggest that you use BTG's tagging feature to focus on each topic.
Here are all of the questions tagged as counting questions: https://www.beatthegmat.com/forums/tags/ ... mbinations
Here are the probability questions: https://www.beatthegmat.com/forums/tags/ ... robability
(see the left side of that linked page for more tag options.)

Spend A LOT of time reviewing the responses from the Experts on this site. They typically model the steps one should take when tackling math problems.

Cheers,
Brent