Someone damaged the flag

Probability Level 2

Assume you have a USA flag. Also assume that it is magical. Why? Because this is a maths problem.

So the USA flag has 50 stars, positioned in 9 rows, the odd-numbered rows have 6 stars each, while the other have 5 stars each.

And so someone (maybe your pesky little brother) knocked the stars off the flag. He also made all the stars distinct by writing a number 1 to 50 on each star.

How many ways can you put back the stars into 9 rows, the odd-numbered rows have 6 stars each, while the other have 5 stars each?

Round to 3 significant figures

Note: Stars are distinct Rows are distinct Position on rows are not distinct (i.e. first in first row is no different from second in first row)

6.02 \times 10^{23}

1.84 \times 10^{54}

7.58 \times 10^{41}

3.04 \times 10^{64}

1 0

1 solution

展豪張
Mar 20, 2016

The answer is $\dfrac{50!}{(6!)^5\times(5!)^4}$

Someone damaged the flag

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