The number of different groups of cookies he can choose from the 12 cookies is 220
How to determine the number of different groups of cookies he can choose from the 12 cookies?
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
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