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# Stuck on a permutation question, help!! watch

1. Hi guys, basically, there's a permutation question that i dont understand, the q is:

Suppose repetitions are not permitted.
(a) Find the number of three-digit numbers that can be formed from the six digits 2,3,4,5,6,7 and 9.

(b) how many of them are less than 400?

(c) how many of them are even.

(A) P(6,3) - CAN SOMEONE EXPLAIN THAT TO ME?

(B) 2*5*4

(C) 2*5*4

I would really appreciate if someone could explain the answers to me

thanks!!
2. (Original post by mabz123)
Hi guys, basically, there's a permutation question that i dont understand, the q is:

Suppose repetitions are not permitted.
(a) Find the number of three-digit numbers that can be formed from the six digits 2,3,4,5,6,7 and 9.

(b) how many of them are less than 400?

(c) how many of them are even.

(A) P(6,3) - CAN SOMEONE EXPLAIN THAT TO ME?

(B) 2*5*4

(C) 2*5*4

I would really appreciate if someone could explain the answers to me

thanks!!
You have listed 7 digits not 6. Assuming there are 6 digits:

Think of the choices you have for each digit. a) For the first digit there are 6 choices, the second digit then has 5 choices since this digit cannot be the same as the first. Then for the third digit there are 4 choices.

Multiplying these together you have 6 x 5 x 4 = 120 choices for the 3 digit number. This is the same as P(6,3).

Have a go at b) and c) now.

EDIT : The answer to c) looks like a mistake. Check you've written the question correctly.
3. For c) it might be helpful to choose the digits in reverse order. But I get 3*5*4 bit confused. 3 being the number of even numbers from the list to choose from.

@notnek, thanks for the explanation, i get it now.
5. (Original post by notnek)
...
i have another question, i was wondering if you would be able to help me with it.

The question is:

A women student is to answer 10 out of 13 questions. Find the number of her choices where she must answer:

(a) the first two questions
(b) the first or second question but not both
(c) Exactly three out of the first 5 question
(d) atleast 3 of the first 5 questions

(a) 165
(b) 110
(c) 80
(d) 276

i'd really appreciate if someone could explain these answers to me.

thanks!
6. (Original post by mabz123)
i have another question, i was wondering if you would be able to help me with it.

The question is:

A women student is to answer 10 out of 13 questions. Find the number of her choices where she must answer:

(a) the first two questions
(b) the first or second question but not both
(c) Exactly three out of the first 5 question
(d) atleast 3 of the first 5 questions

(a) 165
(b) 110
(c) 80
(d) 276

i'd really appreciate if someone could explain these answers to me.

thanks!
a) She has no choice for the first 2 questions. There are 8 more questions that she can choose out of 11 choices. Order mattered in your first question but doesn't here (choosing question 1 then 2 then 3 is no different from choosing 2 then 3 then 1). So this is a combination problem and the answer is 11 C 8 (11 choose 8) = 165.

See if you can do the rest of the questions now.
7. (Original post by notnek)
a) She has no choice for the first 2 questions. There are 8 more questions that she can choose out of 11 choices. Order mattered in your first question but doesn't here (choosing question 1 then 2 then 3 is no different from choosing 2 then 3 then 1). So this is a combination problem and the answer is 11 C 8 (11 choose 8) = 165.

See if you can do the rest of the questions now.
ok, so i got the answer to b, and i got it by doing 2*C(11,9)
8. (Original post by mabz123)
ok, so i got the answer to b, and i got it by doing 2*C(11,9)
There are C(5,3) for the first 3 questions. Since there must be exactly 3 chosen from the first 5, the remaining 7 questions can only be chosen from 13-5 = 8 choices.

Can you finish it?
9. (Original post by mabz123)
Hi guys, basically, there's a permutation question that i dont understand, the q is:

Suppose repetitions are not permitted.
(a) Find the number of three-digit numbers that can be formed from the six digits 2,3,4,5,6,7 and 9.

(b) how many of them are less than 400?

(c) how many of them are even.

(A) P(6,3) - CAN SOMEONE EXPLAIN THAT TO ME?

(B) 2*5*4

(C) 2*5*4

I would really appreciate if someone could explain the answers to me

thanks!!
The answer to (c) should be 3 x 5 x 6
10. (Original post by brianeverit)
The answer to (c) should be 3 x 5 x 6
I got 3x5x4. The third digit is chosen from the 3 even numbers, the second digit is then chosen from the remaining 5 (even or odd) numbers and the first digit chosen from the remaining (even or odd) 4 numbers.
11. (Original post by steve44)
I got 3x5x4. The third digit is chosen from the 3 even numbers, the second digit is then chosen from the remaining 5 (even or odd) numbers and the first digit chosen from the remaining (even or odd) 4 numbers.
My answer was because you had listed 7 integers 2,3,4,5,6,7 & 9
12. (Original post by brianeverit)
My answer was because you had listed 7 integers 2,3,4,5,6,7 & 9
Oh right. I'm not the OP by the way - it's not my list. And I think we concluded near the start of the thread (see notnek's first post) that there should only be 6 numbers there, because otherwise the answers to (a) (and (b)) would be wrong. Personally I just automatically omitted the 9 but didn't say so...now come to think of it if I'd omitted one of the even numbers from the list (maybe either the 4 or the 6 so as not to change the answer to part (b)) the answer stated in the question for part (c) wouldn't be wrong...

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