write all the groupings of numbers 1 - 50 into groups of 7

M

minnie

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Jul 29, 2007
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Yesterday, my parents asked me this question:

Write all the ways the numbers 1 through 50 can be arranged into groups of 7.

For instance, {1, 2, 3, 4, 5, 6, 7} or {2, 3, 4, 5, 6, 7, 1}, etc. I wrote as many as I could think of, but my parents said it wasn't enough.

I want to see and know how many differents ways the numbers can be arranged into groups of 7.
 
JW is exactly correct. You sure have a lot of listing to do.

You're parents were right. You have a long way to go.

The general formula for choosing r items out of n when order matters is

\(\displaystyle \L\\\frac{n!}{(n-r)!}\)

In your case, n=50 and r=7.

\(\displaystyle \L\\\frac{50!}{43!}\)

\(\displaystyle \L\\\frac{(50)(49)(48)(47).......(2)(1)}{(43)(42)(41)(40)....(2)(1)}\)

After the cancellations you are left with what JW gave you.

A big number. 503,417,376,000
 
seconds in 1 year = 31,556,926 (includes leap years et al...)

503,417,376,000 / 31,556,926 = 15,952.67.....

Sooo...if you can do 1 per second, it'll take you a modest ~15,953 years :idea:
 
Now do the next calculation.

If you wrote all the numbers in a row on a strip of paper and you wrote 10 characters in an inch - including the commas separating and assume all the numbes are two digits like 01, 02, etc.)

How long the strip will have to be - can it cover the distance from here to the moon?

From here to the sun?
 
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