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Project Euler Homework
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How many values of C(n,r), for 1 <= n <= 100, exceed one-million? More...
#include <iostream>Go to the source code of this file.
Classes | |
| class | ncr_million |
Functions | |
| int | main () |
Variables | |
| const int | N = 100 |
How many values of C(n,r), for 1 <= n <= 100, exceed one-million?
There are exactly ten ways of selecting three from five, 12345:
123, 124, 125, 134, 135, 145, 234, 235, 245, and 345
In combinatorics, we use the notation, 5C3 = 10.
In general,
![\[C^n_r = \frac{n!}{r!(n−r)!}\]](form_33.png)
,where r ≤ n, n! = n×(n−1)×...×3×2×1, and 0! = 1.
It is not until n = 23, that a value exceeds one-million: 23C10 = 1144066.
How many, not necessarily distinct, values of nCr, for 1 ≤ n ≤ 100, are greater than one-million?
Definition in file 053.cpp.
1.7.3