1. ## Counting question

I have two set of solutions, which one has answered the question correctly?

Solution 1:

Solution 2:

Please correct where wrong if both are wrong, thanks

2. ## Re: Counting question

Originally Posted by inayat
I have two set of solutions, which one has answered the question correctly?
Please correct where wrong if both are wrong, thanks
Can you please type the post?

3. ## Re: Counting question

Originally Posted by Plato
Can you please type the post?
Solution 1:

Order matters since sequence 0,1,2,3,4 is different from 1,0,2,3,4
Repetition is allowed since we are not given explicitly that repetition is not allowed

a) No. of sequences = 16^5
b) No. of sequence = p(16,6) = 16!/10!= 16x14x15x14x13x12x11
c) No. of sequence = total sequence - (no. of sequence having all numbers - no. of sequence having all letters)
= 16^5 - 10^5 -6^5

Please let me know which one is correct or how it should be answered where wrong.

Thanks

4. ## Re: Counting question

Originally Posted by inayat
Ya ya...I'm sure YOU can read it...

5. ## Re: Counting question

Originally Posted by DenisB
Ya ya...I'm sure YOU can read it...
Lol excuse me?
It is though xD

6. ## Re: Counting question

Originally Posted by inayat
Solution 1:

Order matters since sequence 0,1,2,3,4 is different from 1,0,2,3,4
Repetition is allowed since we are not given explicitly that repetition is not allowed

a) No. of sequences = 16^5
b) No. of sequence = p(16,6) = 16!/10!= 16x14x15x14x13x12x11
c) No. of sequence = total sequence - (no. of sequence having all numbers - no. of sequence having all letters)
= 16^5 - 10^5 -6^5
All of those answers are correct.

What is the question that goes with solution #2?

7. ## Re: Counting question

Originally Posted by Plato
All of those answers are correct.

What is the question that goes with solution #2?
Its my friends working out for the same question and i want to know whether his is right and if not, why.

8. ## Re: Counting question

Originally Posted by inayat
Its my friends working out for the same question and i want to know whether his is right and if not, why.
Again I cannot read your writing. You seen to have a good grasp on parts a) & b)!

for part c) "at least one of each"
There are $\large{10^5+6^5}$ strings of either all digits or all letters. Subtract that from the total to get at least one of each.

9. ## Re: Counting question

Originally Posted by Plato
Again I cannot read your writing. You seen to have a good grasp on parts a) & b)!

for part c) "at least one of each"
There are $\large{10^5+6^5}$ strings of either all digits or all letters. Subtract that from the total to get at least one of each.
For part b)

Would it be 16!/11! or 16!/10! ?

10. ## Re: Counting question

Originally Posted by inayat
For part b)
Would it be 16!/11! or 16!/10! ?
Do you understand that a permutation of $n$ taken $k,~0\le k\le n$ at a time is $\large{^n\mathcal{P}_k=\dfrac{n!}{(n-k)!}}~?$

The correct answer for (b) is $\large{^{16}\mathcal{P}_5}$