Question

~QUIZ~
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Soal:
There are 15 toppings to choose from at a pizza restaurant. You plan to order a 4-topping pizza. How many different pizzas could you order?
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Syarat untuk menjawab soal :
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Answer 1

Jawab:
There are 1,365 different pizzas that
can be ordered

Penjelasan dengan langkah-langkah:
Given that there are 15 different toppings
n = 15

You choose 4 toppings out of those 15
r = 4

Find how many different pizzas that can
be ordered (C(n, r))

C(n, r) = n!/(r!(n-r)!)
C(15, 4) = 15!/(4!(15-4)!)
C(15, 4) = 15!/(4!11!)
C(15, 4) = 15·14·13·12·(11!/(4!11!))
C(15, 4) = 15·14·13·12/(4!)
C(15, 4) = 32,760/(4(3)(2))
C(15, 4) = 1,365

There are 1,365 different pizzas that
can be ordered (xcvi)

Answer 2

Verified answer

Option = 15 toppings

Choice = 4-topping pizza

Combination:

[tex]C_{n,r} =\frac{n!}{r!(n-r)!} \\\\C_{15,4} =\frac{15!}{4!(15-4)!}\\\\=\frac{15\times {14\times{13\times{12\times{11!}}}}}{(4\times{3\times{2\times{1}}})11!}\\\\=\frac{15\times {14\times{13\times{12}}}}{4\times{3\times{2}}}[/tex]

= 32760/24

= 1365 pizzas

So, the pizza that I can order is 1365 different pizzas.