Ams 310 Survey Of Probability And Statistics Worksheet - Midterm Exam I - Stony Brook University Page 8
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11(6) (a). How many ways to make a 6 letter password without repetition?
(b). How many ways to make a 6 letter password allowing repetition?
(c). How many ways to form a committee with two women and two men from total
of eight women and ten men.
Solution:
(a). There are 26 letters. To select 6 for password is a permutation
N =
P
.
26
6
(b). When repetition is allowed, each letter in the password has 26 choices. Since
each pick-up is independent of other pick-ups, therefore the number of ways is
6
N = 26
.
(c). The process can be decomposed into two stages: select two women from the
eight women; and then select two men from the 10 men.
8
10
N =
2
2
8
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