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Unformatted text preview: 8 digit numbers with prime digits? 48
Example: In a group of 23 people, how likely is it that they all have
their birthdays on a different date? Math 30530 (Fall 2012) Counting September 13, 2013 9 / 12 Selecting k items from n, WITH REPLACEMENT
In how many ways can we pull out k items from among n different,
distinct objects, if each time we pull out an item, we note it and put it
back?
Order matters: (we produce a list (ﬁrst item, second, . . ., last))
nk
Example: 8 digit numbers with prime digits? 48
Example: In a group of 23 people, how likely is it that they all have
their birthdays on a different date?
ways of choosing 23 different dates, in order
ways of choosing 23 dates, in order
365×364×...×343
= 365×365×...×365
≈ .4927 < 50%
Math 30530 (Fall 2012) Counting September 13, 2013 9 / 12 Selecting k items from n, WITH REPLACEMENT
In how many ways can we pull out k distinct items from among n
different, distinct objects? Math 30530 (Fall 2012) Counting September 13, 2013 10 / 12 Selecting k items from n, WITH REPLACEMENT
In how many ways can we pull out k distinct items from among n
different, distinct objects?
Order doesn’t matter: (we just note how many of the ﬁrst item,
how many of the second, etc.)
n+k −1
k Math 30530 (Fall 2012) Counting September 13, 2013 10 / 12 Selecting k items from n, WITH REPLACEMENT
In how many ways can we pull out k distinct items from among n
different, distinct objects?
Order doesn’t matter: (we just note how many of the ﬁrst item,
how many of the second, etc.)
n+k −1
k
Example: Select 8 singledigit primes, no particular order?
11
8 Math 30530 (Fall 2012) = 165 Counting September 13, 2013 10 / 12 Some examples
I have 36 identical prizes to distribute to the class (53 people). All I
care about is how many prizes each student gets. How many
possible ways to distribute are there? Math 30530 (Fall 2012) Counting September 13, 2013 11 / 12 Some examples
I have 36 identical prizes to distribute to the class (53 people). All I
care about is how many prizes each student gets. How many
possible ways to distribute are there?
Here n = 53 (I’m choosing from pool of students), r = 36 (I’m
choosing students to give prizes to), and I’m choosing with
replacement, order not mattering, so solution is
53 + 36 − 1
36 Math 30530 (Fall 2012) = Counting 88
36 ≈ 6 × 1034 September 13, 2013 11 / 12 Some examples
I hav...
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 Fall '08
 Hind,R
 Counting, Probability

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