Permutation-Combination

[nahid078]

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

[MartyMurray]

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

This question requires finding not just the number of permutations one can create with the six flags together but also the number of permutations one can create with fewer than six flags.

1 Flag At A Time

6 Signals

2 Flags At A Time

6 x 5 = 30 Signals

3 Flags At A Time

6 x 5 x 4 = 120 Signals

4 Flags At A Time

6 x 5 x 4 X 3 = 360 Signals

5 Flags At A Time

6 x 5 x 4 X 3 x 2 = 720 Signals

6 Flags At A Time

6 x 5 x 4 X 3 x 2 x 1 = 720 Signals

So we get 6 + 30 + 120 + 360 + 720 + 720 = 1956 Unique Signals

Choose b.

[Brent@GMATPrepNow]

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

--------------------------

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]

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.

[ravihanda]

If you can only use one flag, you can give 6 signals.
If you can use two flags, you can give 6*5 = 30 signals
If you can use three flags, you can give 6*5*4 = 120 signals
If you can use four flags, you can give 6*5*4*3 = 360 signals
If you can use five flags, you can give 6*5*4*3*2 = 720 signals
If you can use six flags, you can give 6*5 = 720 signals

Total number of signals = 720 + 720 + 360 + 120 + 30 + 6 = 1956. Option B

[Brent@GMATPrepNow]

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

[MartyMurray]

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.

Actually your not being comfortable with this would not hurt your score significantly. On the entire test you see, there will likely be only a few, maybe even just one or two questions that require much knowledge of these concepts and application of them.

As far as probability goes, the key basic concept that you need to understand is that the probability of an event or set of events occurring is the ratio of the number of those favorable outcomes to the number of all possible outcomes.

Much of the rest of what you need to understand is somehow based on what Brent calls the Fundamental Counting Principle. By getting to understand that and how it can be applied, you can at least build a foundation of skills for doing many of these types of problems.

Other than that, if your test is around a week away, you might be better off working on things that you can apply more generally on the test.