# Did I do this correctly?

• Jan 30th 2010, 05:42 PM
jmedsy
Did I do this correctly?
There are 40 students in our combinatorics class. Use combinatorial principles to compute the probability that at least two people in class have the same birthday (assume 365 days in a year)...

100% * summation from i=2 to 40 of ((40 choose i) * (1/365)^i * (364/365)^(40-i))

is equal to (by the binomial theorem)

100% * ((1/365 + 364/365)^40 - (40 choose 0) * (1/365)^0 * (364/365)^40 - (40 choose 1) * (1/365) * (364/365)^39)

= .546%
• Jan 30th 2010, 06:37 PM
mr fantastic
Quote:

Originally Posted by jmedsy
There are 40 students in our combinatorics class. Use combinatorial principles to compute the probability that at least two people in class have the same birthday (assume 365 days in a year)...

100% * summation from i=2 to 40 of ((40 choose i) * (1/365)^i * (364/365)^(40-i))

is equal to (by the binomial theorem)

100% * ((1/365 + 364/365)^40 - (40 choose 0) * (1/365)^0 * (364/365)^40 - (40 choose 1) * (1/365) * (364/365)^39)

= .546%