Arturo can select the days on which to have pizza in 70 ways using combination rule if he chooses any four of the next eight days.
What is combination?
A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
In combinations, one can select the items in any order.
Number of combination of a objects chosen from n objects
ⁿCₐ = [tex]\frac{n!}{a! (n-a)!}[/tex]
According to the given question:
To select 4 days out of the next 8 days, use combination rule
ⁿCₐ = [tex]\frac{n!}{a! (n-a)!}[/tex]
⁸C₄ = [tex]\frac{8!}{4! (8-4)!}[/tex]
⁸C₄ = (8x7x6x5x4x3x2x1)/(4x3x2x1)(4x3x2x1)
⁸C₄ = (8x7x6x5)/(4x3x2x1)
⁸C₄ = 70
Therefore there are 70 ways Arturo can select the 4 days out of 8 to have pizza for dinner.
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