There are 12 different cookies on a plate. Aiden will choose 3 of these cookies to pack in his lunch. How many different groups

Question

1 year ago

12

of cookies can he choose from 12?
A) 220
B) 320
C) 420
D) 440
I know the correct answer is A) 220, but I am not sure why?

1 answer:

kupik [55] · Answer 1 · 2023-12-07T00:57:23+03:00

The number of different groups of cookies he can choose from the 12 cookies is 220

<h3>How to determine the number of different groups of cookies he can choose from the 12 cookies?</h3>

The given parameters are:

Number of cookies, n = 12

Selected cookies, r = 3

The number of different groups of cookies he can choose from the 12 cookies is calculated as:

Numbers = 12C3

The combination formula is represented as:

nCr = n!/(n - r)!r!

Substitute the known values in the above equation

Numbers = 12!/(12 - 3)!3!

Evaluate the difference in the above equation

Numbers = 12!/9!3!

Expand the above equation

Numbers = 12*11*10*9!/9!3!

Evaluate the quotient

Numbers = 12*11*10/3!

Expand the above equation

Numbers = 12*11*10/3*2*1

Evaluate the products

Numbers = 1320/6

Evaluate the quotients

Numbers = 220

Hence, the number of different groups of cookies he can choose from the 12 cookies is 220

So, the complete parameters are:

Number of cookies, n = 12

Selected cookies, r = 3

Number of selection = 220