combination problems : Order is Important or Not?

[summer101.blues]

Hi All,

While solving combination problems, I always get confused whether Order is Important or Not. Can anyone please explain this topic!

For Ex. in the below question, why is order important?

A four character password consists of one letter of the alphabet and three different digits between 0 & 9, inclusive. The letter must appear as the second or third character of the password. How many different passwords are possible?
A. 5040
B. 18720
C. 26000
D. 37440
E. 52000

[magoood_2020]

Hi All,

While solving combination problems, I always get confused whether Order is Important or Not. Can anyone please explain this topic!

For Ex. in the below question, why is order important?

A four character password consists of one letter of the alphabet and three different digits between 0 & 9, inclusive. The letter must appear as the second or third character of the password. How many different passwords are possible?
A. 5040
B. 18720
C. 26000
D. 37440
E. 52000

Common sense is needed to see if order matters or not! regarding passwords then of course order DOES matter!

Since there's a word "OR" in "he letter must appear as the second or third character of the password" sentence, then this is a good indicative to make 2 cases (one case for the letter being the 2nd position and another for the letter being the 3rd)

case i

Make 4 slots on your paper where 2nd slot can be filled in 26 ways, 1st can be any digit from 10 digits so it can be filled in 10 ways, 3rd slot can be filled in 9 ways (remember you consumed a digit already in 1st slot), 4th slot can be filled in 8 ways: Total ways for case i = 18720

case ii

Make 4 slots on your paper where 3rd slot can be filled in 26 ways, 1st can be any digit from 10 digits so it can be filled in 10 ways, 2nd slot can be filled in 9 ways, 4th slot can be filled in 8 ways: Total ways for case i = 18720

Total passwords: 37440

[RonPurewal]

Common sense is needed to see if order matters or not! regarding passwords then of course order DOES matter!

^^^ that's pretty much it.

it will usually be clear from context whether order matters or not. just ask yourself: "if i scramble the outcome, do i get the same outcome, or is it legitimately a different outcome?"
if it's the former, then order is irrelevant. if it's the latter, then order matters.

if you scramble a password -- e.g., from ABCDE to ECDBA -- then that's clearly a different password, so order matters in that case.

on the other hand, if a committee consists of Alice, Bob, and Carl, then that's the same situation as if the committee consists of Bob, Carl, and Alice.

etc.

[sherlock]

[redacted]

The above question should clear your doubts, according to this , just make 3 slots on your scratch paper, and remember that there are total 8 choices to choose from first and then 6 choices(as one pair of same color car is removed) and then 4 choices (as 2 pairs are removed). Now just think whether order is important or not, for doing that, think is (Blue, Green, Red) different from (Green, Blue, Red), (Red, Green, Blue)...no,right! So,in this case order is not important. So, the final answer would be,
(8*6*4)/3! = 32
Why 3! ? Because every group of 3 can be arranged in 3! ways!

Hope it helps!

[RonPurewal]

shubham, we need a citation of the original source for EVERY question posted in this folder -- even if you're just posting the question as a "reference".

please familiarize yourself with the forum rules. thanks.

__

also -- why are you responding to a discussion that has been dormant for more than 3 years?