A student has 13 writing instruments: 7 pencils, 4 bright pink pens, and 2 giant pens. How many ways can a selection be mad if no more than 1 bright pink pen is selected?

Question

anonymous · Answer

@jim_thompson5910

jim_thompson5910 · Answer

How many things are you grabbing again?

anonymous · Answer

Out of 13

jim_thompson5910 · Answer

yes

anonymous · Answer

What?

jim_thompson5910 · Answer

you have 13 items total, how many of these items are you selecting?

jim_thompson5910 · Answer

Ok it doesn't say that at the top

anonymous · Answer

Sorry about that, we are choosing 1 out of the 4

jim_thompson5910 · Answer

not sure what you mean

jim_thompson5910 · Answer

oh the pink pens you mean?

anonymous · Answer

It says if no more than 1 pink pen is selected and there are 4 pink pens

anonymous · Answer

Help!! Please!

jim_thompson5910 · Answer

i'm guessing this is part b) or c) of a problem?

anonymous · Answer

Yes

jim_thompson5910 · Answer

You have 2 cases

Case 1) You choose 0 pink pens

So you have 13 - 4 = 9 items to pick from. 

So you have 9 C 4 = (9!)/(4!(9-4)!) = 126 ways to do this option

-------------------------------------------

Case 2) You choose 1 pink pen

So you lock in 1 slot (for that pink pen) leaving you 4-1 = 3 slots. You have 7+2 = 9 items left to choose from

So you have 9 ncr 3 = (9!)/(3!(9-3)!) = 84 ways to do this

Since that exhausts all possible scenarios, you just add up the counts to get: 126+84 = 210

jim_thompson5910 · Answer

This is of course assuming that you can distinguish between the pencils and pens.

anonymous · Answer

That makes sense, but it is saying that choosing 1 pink pen is not 210, 126, or 86

jim_thompson5910 · Answer

so what are your answer choices?

anonymous · Answer

There aren't any answer choices

jim_thompson5910 · Answer

so it's just saying that those answers are incorrect?

jim_thompson5910 · Answer

if possible, post a screenshot of the problem

anonymous · Answer

Yes

jim_thompson5910 · Answer

is that possible?

anonymous · Answer

attachment

jim_thompson5910 · Answer

oh it's 2 selections instead of 4, i see

anonymous · Answer

How would I solve it?

jim_thompson5910 · Answer

how did you get 1287 for part 1?

anonymous · Answer

Part one was out of 8 instead of 13

jim_thompson5910 · Answer

but it says "...select 2 writing implements", I don't see 8 anywhere

anonymous · Answer

Sorry, answering a different problem there. The answer is actually 72 for part 1. But not sure about part 2

jim_thompson5910 · Answer

you mean 78?

anonymous · Answer

yes

jim_thompson5910 · Answer

for part 2), add 9 C 2 = 36 to (4 C 1)*(9 C 1) = 36 to get   36+36 = 72

So the answer to part 2) is 72

anonymous · Answer

What if it was out of 8 instead of 2 for part 1? Wouldn't it be (4C1)*(9C1)=36+ 9C8=36+9=45

jim_thompson5910 · Answer

it would be

13 C 8 = 1287

anonymous · Answer

What about for part 2?

jim_thompson5910 · Answer

this is for part 1

jim_thompson5910 · Answer

part 2)

9 C 8 + (4 C 1)*(9 C 7) = 9 + 4*36 = 153

anonymous · Answer

That worked! You are a lifesaver! Could you just explain it though?

jim_thompson5910 · Answer

Case 1) You choose 0 ball point pens

So there are 9 C 8 = 9 ways to do this 

-------------------------------------------------------

Case 2) You choose 1 ball point pen

There are 4 C 1 = 4 ways to choose exactly 1 ball point (of the 4). There are 9 C 7 = 36 ways choose the remaining writing implements

So there are 4*36 = 144 ways to carry out case 2)

Add up the counts to get: 9 + 144 = 153

anonymous · Answer

Thank!

jim_thompson5910 · Answer

np