An icecream vendor sells 15 flavors of icecream. You want to sample AT LEAST 4 of the flavors. How many different combos of ice cream flavors can you sample?
I know you can add 15C4 + 15C5 + ... + 15C15 = 32192...
but there's also ANOTHER way of doing it. which is the "TOTAL - (the ones NOT 4)"
For ex: TOTAL - (15C0 + 15C1 + 15C2 + 15C3) = 32192
the second way is shorter. and for the "TOTAL" someone got (2^15)=32768.
My question is HOW did they get "(2^15)"...? i know "15" is from the total flavors... but is "2" from either "YES" trying it and "NO" to trying it???
PLEASEEE EXPLAINN!! thank you!!
I know you can add 15C4 + 15C5 + ... + 15C15 = 32192...
but there's also ANOTHER way of doing it. which is the "TOTAL - (the ones NOT 4)"
For ex: TOTAL - (15C0 + 15C1 + 15C2 + 15C3) = 32192
the second way is shorter. and for the "TOTAL" someone got (2^15)=32768.
My question is HOW did they get "(2^15)"...? i know "15" is from the total flavors... but is "2" from either "YES" trying it and "NO" to trying it???
PLEASEEE EXPLAINN!! thank you!!
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You got the reasoning right, but I think you just could not justify it ....
Imagine all 15 flavors in a line, and you can asign a 'yes' or 'no'
label for each to make your selections .... that will permit any
combination from zero to all 15 flavors selected. Since all the 15
need to be asigned a yes or no, it is 2^15 possibilities.
Then, you just need to subtract the following ....
==> 15C0 = 1
==> 15C1 = 15
==> 15C2 = 105
==> 15C3 = 455
==> 2^15 - (1 + 15 + 105 + 455) = 32192 .... answer
Imagine all 15 flavors in a line, and you can asign a 'yes' or 'no'
label for each to make your selections .... that will permit any
combination from zero to all 15 flavors selected. Since all the 15
need to be asigned a yes or no, it is 2^15 possibilities.
Then, you just need to subtract the following ....
==> 15C0 = 1
==> 15C1 = 15
==> 15C2 = 105
==> 15C3 = 455
==> 2^15 - (1 + 15 + 105 + 455) = 32192 .... answer