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Q. Assume a birthday is equally likely to occur in each of the 365 days. In a group of 30 people, what is the probability that no two have birthdays on the same day?
Solution: Let S be the set of all possible birthdays for the 30 people. Since the first person can have their birthday on any of 365 days, as does the second, third and so on until the 30th person,
How many ways can every person have a different birthday? In this situation, there are 30 different days which can be someone's birthday. So the number of ways to have 30 different birthdays is 365C30.
The probability of every person having a different birthday is equal to
This means that there is nearly zero probability that none of the thirty people will share a birthday! This is why it is so common that you will share a birthday with someone else in your math class.
Case 1: Suppose we have two terms 8ab and 4ab. On dividing the first by the second we have 8ab/4ab = 2 or 4ab/8ab = (1/2) depending on whether we consider either 8ab or 4ab as the
How many ways can six men and three women form a line if no two women may stand behind each other?
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arrange these numbers in ascending order. -5 -7 1 2 15 0 - 25
In the previous section we looked at the method of undetermined coefficients for getting a particular solution to p (t) y′′ + q (t) y′ + r (t) y = g (t) .....................
1/a+b+x =1/a+1/b+1/x a+b ≠ 0 Ans: 1/a+b+x =1/a+1/b+1/x => 1/a+b+x -1/x = +1/a +1/b ⇒ x - ( a + b + x )/ x ( a + b + x ) = + a + b/ ab ⇒
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