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I don't understand this problem:

  • A software company sells 23 softwares
  • 7 of these 23 softwares are bestsellers

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.

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    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? – 2017-01-22
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    Zero combinations, since with a maximum of $3$ softwares you can never a bundle of $10$!!! – 2017-01-22
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    Actually I think his meaning from at least 2 and maximum 3 from best selling. And remaining from others to create bundle. – 2017-01-22
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    I meant Bestsellers, sry – 2017-01-22

1 Answers 1

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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

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    So I have 21*12870=270270 for the first case and 35*11440=400400 for the second case and as result I become 270270*400400=108216108000 – 2017-01-22
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    Sorry my mistake I write terms opposite. Wait I can solve for you. – 2017-01-22
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    @Jones876 you should add the two terms you calculated, not multiply! – 2017-01-22
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    Yes your calculation are right. Combine means add two results. 270270 + 400400 = ? – 2017-01-22
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    670670. You're right. Thanks Kanwaljit!!! :) – 2017-01-22
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    Mine pleasure :-) – 2017-01-22