Respuesta :

The number of combinations with repetition that are allowed if n = 4 and r = 3 is given by: Option A: 20

How many k-element combinations of n objects, with repetition can be formed?

The number of  k-element combinations of n objects, with repetition is:

[tex]\overline{C}_{n,k} = \: ^{n + k-1}C_{k} = \dfrac{(n+k-1)!}{k! \times (n-1)!}[/tex]

For this case, we're given that:

  • n = 4
  • k = 3 (the question uses the notation 'r' instead of 'k')

Thus, we get:

[tex]\overline{C}_{n,k} = \dfrac{(n+k-1)!}{k! \times (n-1)!} = \dfrac{(4+3-1)!}{3! \times (4-1)!} \\\\\overline{C}_{n,k} = \dfrac{6!}{3!. 3!} = 20[/tex]

Thus, the number of combinations with repetition that are allowed if n = 4 and r = 3 is given by: Option A: 20

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