THE NUMBER OF WAYS IN WHICH AN EXAMINER CAN ASSIGN 30 MARKS TO 8 QUESTIONS GIVING NOT LESS THAN 2 MARKS FOR EACH QUESTION IS
I DON'T KNOW
but
If you put 2 on each question to start with that is 16 points,
the question becomes,
How many ways can you allocate 14 marks to 8 questions.
14,0,0,0,0,0,0,0 8 ways
13,1,0,0,0,0,0,0 8!/6! = 56
12,2 56
12,1,1 8!/(5!2!) =168
11,3 56
11,2,1 $${\frac{{\mathtt{8}}{!}}{{\mathtt{5}}{!}}} = {\mathtt{336}}$$
11,1,1,1, $${\frac{{\mathtt{8}}{!}}{\left({\mathtt{4}}{!}{\mathtt{\,\times\,}}{\mathtt{3}}{!}\right)}} = {\mathtt{280}}$$
10,4 56
10,3,1 336
10,2,2 $${\frac{{\mathtt{8}}{!}}{\left({\mathtt{5}}{!}{\mathtt{\,\times\,}}{\mathtt{2}}{!}\right)}} = {\mathtt{168}}$$
10,2,1,1 $${\frac{{\mathtt{8}}{!}}{\left({\mathtt{4}}{!}{\mathtt{\,\times\,}}{\mathtt{2}}{!}\right)}} = {\mathtt{840}}$$
10,1,1,1,1,
9,5
9,4,1
9,3,2
9,3,1,1
9,2,1,1,1
9,1,1,1,1,1
8,6
8,5,1
8,4,2,
8,4,1,1,
8,3,3
8,3,2,1
8,3,1,1,1,
8,2,2,2
8,2,2,1,1
8,2,1,1,1,1,
8,1,1,1,1,1,1,
7,7
7,6,1
7,5,2
7,5,1,1
7,4,3,
7,4,2,1
7,4,1,1,1,
7,3,3,1
7,3,2,2
7,3,2,1,1,
7,3,1,1,1,1,
7,2,2,1,1,1,
7,2,1,1,1,1,1,
7,1,1,1,1,1,1,1,
6,5,3
6,5,2,1
6,5,1,1,1
6,4,4,
6,4,3,1
6,4,2,2,
6,4,2,1,1,
6,4,1,1,1,1,
6,3,3,2
6,3,3,1,1
6,3,2,2,1
6,3,2,1,1,1,
6,3,1,1,1,1,1,
6,2,2,2,2
6,2,2,2,1,1
6,2,2,1,1,1,1,
6,2,1,1,1,1,1,1
5,5,4
5,5,3,1
5,5,2,2
5,5,2,1,1,
5,5,1,1,1,1,
5,4,4,1
5,4,3,2
5,4,3,1,1
5,4,2,1,1,1
5,4,1,1,1,1,1
5,3,3,3
5,3,3,2,1
5,3,3,1,1,1,
5,3,2,1,1,1,1
5,3,1,1,1,1,1,1,
5,2,2,2,2,1
5,2,2,2,1,1,1,
5,2,2,1,1,1,1,1,
4,4,4,2
4,4,4,1,1,
4,4,3,3
4,4,3,2,1
4,4,3,1,1,1,
4,4,2,1,1,1,1,
4,4,1,1,1,1,1,1,
4,3,3,3,1
4,3,3,2,2,
4,3,3,2,1,1
4,3,3,1,1,1,1,
4,3,2,2,2,1
4,3,2,2,1,1,1,
4,3,2,1,1,1,1,1,
4,2,2,2,2,2
4,2,2,2,2,1,1
4,2,2,2,1,1,1,1,
3,3,3,3,2
3,3,3,3,1,1
3,3,3,2,2,1
3,3,3,2,1,1,1,
3,3,3,1,1,1,1,1,
3,3,2,2,2,2,
3,3,2,2,2,1,1,
3,3,2,2,1,1,1,1,
3,2,2,2,2,2,1
3,2,2,2,2,1,1,1,
2,2,2,2,2,2,2
2,2,2,2,2,2,1,1
TOTAL=
OBVIOUSLY THERE IS A MUCH SIMPLER WAY BUT MAYBE THIS WOULD WORK TOO :) LOL
I DON'T KNOW
but
If you put 2 on each question to start with that is 16 points,
the question becomes,
How many ways can you allocate 14 marks to 8 questions.
14,0,0,0,0,0,0,0 8 ways
13,1,0,0,0,0,0,0 8!/6! = 56
12,2 56
12,1,1 8!/(5!2!) =168
11,3 56
11,2,1 $${\frac{{\mathtt{8}}{!}}{{\mathtt{5}}{!}}} = {\mathtt{336}}$$
11,1,1,1, $${\frac{{\mathtt{8}}{!}}{\left({\mathtt{4}}{!}{\mathtt{\,\times\,}}{\mathtt{3}}{!}\right)}} = {\mathtt{280}}$$
10,4 56
10,3,1 336
10,2,2 $${\frac{{\mathtt{8}}{!}}{\left({\mathtt{5}}{!}{\mathtt{\,\times\,}}{\mathtt{2}}{!}\right)}} = {\mathtt{168}}$$
10,2,1,1 $${\frac{{\mathtt{8}}{!}}{\left({\mathtt{4}}{!}{\mathtt{\,\times\,}}{\mathtt{2}}{!}\right)}} = {\mathtt{840}}$$
10,1,1,1,1,
9,5
9,4,1
9,3,2
9,3,1,1
9,2,1,1,1
9,1,1,1,1,1
8,6
8,5,1
8,4,2,
8,4,1,1,
8,3,3
8,3,2,1
8,3,1,1,1,
8,2,2,2
8,2,2,1,1
8,2,1,1,1,1,
8,1,1,1,1,1,1,
7,7
7,6,1
7,5,2
7,5,1,1
7,4,3,
7,4,2,1
7,4,1,1,1,
7,3,3,1
7,3,2,2
7,3,2,1,1,
7,3,1,1,1,1,
7,2,2,1,1,1,
7,2,1,1,1,1,1,
7,1,1,1,1,1,1,1,
6,5,3
6,5,2,1
6,5,1,1,1
6,4,4,
6,4,3,1
6,4,2,2,
6,4,2,1,1,
6,4,1,1,1,1,
6,3,3,2
6,3,3,1,1
6,3,2,2,1
6,3,2,1,1,1,
6,3,1,1,1,1,1,
6,2,2,2,2
6,2,2,2,1,1
6,2,2,1,1,1,1,
6,2,1,1,1,1,1,1
5,5,4
5,5,3,1
5,5,2,2
5,5,2,1,1,
5,5,1,1,1,1,
5,4,4,1
5,4,3,2
5,4,3,1,1
5,4,2,1,1,1
5,4,1,1,1,1,1
5,3,3,3
5,3,3,2,1
5,3,3,1,1,1,
5,3,2,1,1,1,1
5,3,1,1,1,1,1,1,
5,2,2,2,2,1
5,2,2,2,1,1,1,
5,2,2,1,1,1,1,1,
4,4,4,2
4,4,4,1,1,
4,4,3,3
4,4,3,2,1
4,4,3,1,1,1,
4,4,2,1,1,1,1,
4,4,1,1,1,1,1,1,
4,3,3,3,1
4,3,3,2,2,
4,3,3,2,1,1
4,3,3,1,1,1,1,
4,3,2,2,2,1
4,3,2,2,1,1,1,
4,3,2,1,1,1,1,1,
4,2,2,2,2,2
4,2,2,2,2,1,1
4,2,2,2,1,1,1,1,
3,3,3,3,2
3,3,3,3,1,1
3,3,3,2,2,1
3,3,3,2,1,1,1,
3,3,3,1,1,1,1,1,
3,3,2,2,2,2,
3,3,2,2,2,1,1,
3,3,2,2,1,1,1,1,
3,2,2,2,2,2,1
3,2,2,2,2,1,1,1,
2,2,2,2,2,2,2
2,2,2,2,2,2,1,1
TOTAL=
OBVIOUSLY THERE IS A MUCH SIMPLER WAY BUT MAYBE THIS WOULD WORK TOO :) LOL
I think according to Nauseated, the answer is
Hey Nauseated, Chris and I are still waiting for you to walk us through the logic behind this formula. :/
14 unlabelled marks into 8 labelled questions
$$\dbinom{13}{7}=\dfrac{13!}{7!6!}= 1716 \;ways$$
That has a lot more chance of being correct!
I still don't get these. What have I done wrong ??
If I add up all my possibilities that I have listed and the permutations as well, the number would be way higher!
I have listed all the mark possibilities but not all the permuations of them.
What am I doing wrong ??