11 lines
473 B
Markdown
11 lines
473 B
Markdown
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There are exactly ten ways of selecting three from five, `12345`:
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> 123, 124, 125, 134, 135, 145, 234, 235, 245, and 345
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In combinatorics, we use the notation, `C(5,3) = 10`.
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In general, `C(n,r) = n! / (r!(n?r)!)` ,where `r <= n, n! = n * (n?1) * ... * 3 * 2 * 1`, and `0! = 1`.
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It is not until `n = 23`, that a value exceeds one-million: `C(23,10) = 1144066`.
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How many, not necessarily distinct, values of `C(n,r)`, for `1 <= n <= 100`, are greater than one-million?
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