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Probability Level 3

There are 2380 2380 ways for Brilli the ant to choose 4 4 books from her collection. How many ways can Brilli choose 5 5 books?


The answer is 6188.

Alex Segesta by Alex Segesta , 20, USA

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2 solutions

Steven Perkins
May 11, 2014

Selecting 4 of the collection is computed using combinations. comb(n,4) = n!/4!/(n-4)!

I figured trial and error would be quick enough, so I tried comb(10,4), but it was too low. I tried comb(20,4) but it was too high. Soon I zeroed in on comb(17.4) and it was JUST right.

comb(17,5) = 6188 \boxed{6188}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Another way to see that, is to observe that 2380 = 17 × 7 × 5 × 2 2380 = 17 \times 7 \times 5 \times 2 , which tells us that N N would be close to 17.

Finally, 2380 × 4 ! = 17 × 16 × 15 × 14 2380 \times 4! = 17 \times 16 \times 15 \times 14 .

Calvin Lin Staff - 7 years ago

2380 = N!/(N-4)!4! (N-3)(N-2)(N-1)N = 2380x4! = 57120 = 2^5x3x5x7x17 If N=17, 14x15x16x17 = 57120 => N=17 Then the answer is 17!/12!x5! = 6188

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