Question

A teacher has to distribute 15 pens among 5 of his students such
that student A gets at least 3 and at most 6 pens.In how many
ways can this be done ?

Answer 1

\(\large \color{black}{\begin{align}
& \normalsize \text{A teacher has to distribute 15 pens among 5 of his students such}\hspace{.33em}\\~\\
& \normalsize \text{that student A gets at least 3 and at most 6 pens.In how many }\hspace{.33em}\\~\\
& \normalsize \text{ ways can this be done ?}\hspace{.33em}\\~\\
& a.)\ 495 \hspace{.33em}\\~\\
& b.)\ 77 \hspace{.33em}\\~\\
& c.)\ 417 \hspace{.33em}\\~\\
& d.)\ 435 \hspace{.33em}\\~\\
\end{align}}\)

Answer 2

only student A gets atleast 3 to 6 pens necessarily

Answer 3

lets do 4 cases then
Student A
3
4
5
6

Answer 4

when student A gets 3 pens we have 12 pens to distribute among 4 students

Answer 5

12C4=495

Answer 6

u cant just do that

Answer 7

why are you doing 12 choose 4

Answer 8

cuz i left with 4 students and 12 pens

Answer 9

wait umm from your previous questions, when they ask questions like this does that mean the pens are distinguishable or not?

Answer 10

i think pens are similar/identical

Answer 11

okay phew that makes it a lot simpler

Answer 12

so we have 12 pens and 4 students think about it like stars and bars question

Answer 13

15C3