Combinari - exercitiu rezolvat 5

Sa se afle n daca:

C ⁴_n = 5n(n - 3) / 6

se aplica formula combinarilor: combinari de n luate cate k si rezulta:

=> n! / 4!(n - 4)! = 5n(n - 3) / 6

=> (n - 4)! * (n - 3) * (n - 2) * (n - 1) * n / 1 * 2 * 3 * 4 (n - 4)! = 5n(n - 3) / 6

=> (n - 2) * (n - 1) * n / 24 = 5n / 6  (*4)

=> n * (n - 1) * (n - 2) / 24 = 20n / 24

=> n² – n + n² – 2n = 20n

=> 2n² – 3n = 20n

=> 2n² – 3n - 20n = 0

=> 2n² – 23n = 0

=> n(2n - 23) = 0

sol 1=> n = 0

=> 2n - 23 = 0

=> 2n = 23

sol 2=> n = 23 / 2


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