An elevator starts at the basement of the 12 story building with 10 people and e
ID: 3061872 • Letter: A
Question
An elevator starts at the basement of the 12 story building with 10 people and each one choose one’s stop. Count all the possible red stop button number congurations.
An elevator starts at the basement of the 12 story building with 10 people and each one choose one’s stop. Count all the possible stopping congurations of all 10 people.
An elevator starts at the basement of the 12 story building with 10 people and each one choose one’s stop. Count all the possible stopping congurations of all 10 people if we cannot identify (or don’t care) one from another.
Explanation / Answer
No of ways to select r objects from n objects = nCr = n!/r!*(n-r)!
a)
No of buttons can be from 1 to 10
No of configurations with 10 red buttons = 12C10 = 66
No of configurations with 9 red buttons = 12C9 = 220
No of configurations with 8 red buttons = 12C8 = 495
No of configurations with 7 red buttons = 12C7 = 792
No of configurations with 6 red buttons = 12C6 = 924
No of configurations with 5 red buttons = 12C5 = 792
No of configurations with 4 red buttons = 12C4 = 495
No of configurations with 3 red buttons = 12C3 = 220
No of configurations with 2 red buttons = 12C2 = 66
No of configurations with 1 red buttons = 12C1 = 12
No of all possible red stop button number congurations = No of configurations with 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 red stop buttons = 66 + 220 + 495 + 792 + 924 + 792 + 495 + 220 + 66 +12 = 4082
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