#2015_18 Lets add it!

Probability Level 4

$(1\times 2\times 3\times 4) + (2\times 3\times 4\times 5)+\ldots+ (47\times 48\times 49\times 50) = \ ?$

You may use a calculator for the final step of your working.

The answer is 56377440.

1 solution

Ivan Koswara
Aug 19, 2015

Since it appears simple enough to brute force using computer, that is precisely what I did:

1 2	`>>> sum((n+1)(n+2)(n+3)*(n+4) for n in range(47)) 56377440`

While solving, I didn't notice the similarity with the binomial coefficients $\binom{n}{4}$ .

@Ivan Koswara I disagree with the classification of trivial/boring. The Hockey Stick Identity would be extremely useful here, since we essentially want to find $\sum { i \choose 4 }$ .

Calvin Lin Staff - 5 years, 9 months ago

...that's correct. I concluded too quickly. I guess I shouldn't write solutions when rushed + in a bad mood.

EDIT: Edited the solution to be less condescending.

Ivan Koswara - 5 years, 9 months ago

Lol, I know that feeling. Sometimes it's better to just crawl in to a cave and avoid contact.

Hope you feel better!

Calvin Lin Staff - 5 years, 9 months ago

@Calvin Lin – A cave right about now sounds nice. Warm and damp. Maybe.

Jake Lai - 5 years, 9 months ago

Hey ,Its a mathematical problem and you could solve it by the application of Binomial theorem!

Anandhu Raj - 5 years, 9 months ago

#2015_18 Lets add it!

The answer is 56377440.

1 solution

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