The probability that birthday of 6 different persons
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Step-by-step explanation:
Arrange the people in order of height. Ask the shortest person what month she was born in. Whatever she says, there are 125 ways the string of birthmonths, from next shortest to tallest, can be completed.
We now count the "favourables." There are 11 choices for the other month. And for each choice of other month, there are 25−1 ways the string of birthmonths can be completed to yield a favourable, for not everybody can choose the same month as the shortest person. This gives a total of (11)(31)=341 favourables.
Thus the required probability is 341125. Note that this is different in the denominator from the answer mentioned in the post.
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