Combinations - Math Problem

Question

I don't understand this problem:

Question: How many combinations exist to create a Bundle of 10 Softwares, when this Bundle should contain at least 2 and maximum of 3 bestsellers.

I think there are more steps to solve it, but I don't have any idea.

Do you mean, "at least 2 and maximum of 3 bestsellers", rather than just softwares? Assuming that's the case, could you say how many bundles there are with exactly 2 bestsellers? — pjs36, Jan 22 '17 at 16:33
Zero combinations, since with a maximum of $3$ softwares you can never a bundle of $10$!!! — barak manos, Jan 22 '17 at 16:34
Actually I think his meaning from at least 2 and maximum 3 from best selling. And remaining from others to create bundle. — Kanwaljit Singh, Jan 22 '17 at 16:38

Kanwaljit Singh · Accepted Answer · 2017-01-22T17:26:04.630

0

Case 1 - Contains 2 software out of 7 and remaining 8 from 16.

$\binom 72 × \binom {16}8$

= $\frac{7!}{5! × 2!} × \frac{16!}{8! × 8!}$

= $\frac{7 × 6 × 5!}{5! × 2 × 1} × \frac{16 × 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8!}{8! × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1}$

= $21 × 12870 = 270270$

Case 2 - Contains 3 software out of 7 and remaining 7 from 16.

$\binom 73 × \binom {16}7$

On solving you get 400400.

Combine these two cases to get the result.

270270 + 400400 = 670670

edited Jan 22 '17 at 17:26

answered Jan 22 '17 at 16:36

Kanwaljit Singh

So I have 2112870=270270 for the first case and 3511440=400400 for the second case and as result I become 270270*400400=108216108000 – Jones876 Jan 22 '17 at 17:05
Sorry my mistake I write terms opposite. Wait I can solve for you. – Kanwaljit Singh Jan 22 '17 at 17:20
@Jones876 you should add the two terms you calculated, not multiply! – Laars Helenius Jan 22 '17 at 17:24
Yes your calculation are right. Combine means add two results. 270270 + 400400 = ? – Kanwaljit Singh Jan 22 '17 at 17:27
You're right. Thanks Kanwaljit!!! :)

Mine pleasure :-) – Kanwaljit Singh Jan 22 '17 at 17:38

1 Answers1